Reddit mentions: The best mathematical physics books

Friend asked for a similar list a while ago and I put this together. Would love to see people thoughts/feedback.

Very High Level Introductions:

• Mr. Tompkins in Paperback
  
  • A super fast read that spends less time looking at the "how" but focused instead on the ramifications and impacts. Covers both GR as well as QM but is very high level with both of them. Avoids getting into the details and explaining the why.
    
    
• Einstein's Relativity and the Quantum Revolution (Great Courses lecture)
  
  • This is a great intro to the field of non-classical physics. This walks through GR and QM in a very approachable fashion. More "nuts and bolts" than Mr. Tompkins but longer/more detailed at the same time.
    
    
    Deeper Pop-sci Dives (probably in this order):
    
    
• Quantum Theory: A Very Brief Introduction
  
  • Great introduction to QM. Doesn't really touch on QFT (which is a good thing at this point) and spends a great deal of time (compared to other texts) discussing the nature of QM interpretation and the challenges around that topic.
    
• The Lightness of Being: Mass, Ether, and the Unification of Forces
  
  • Now we're starting to get into the good stuff. QFT begins to come to the forefront. This book starts to dive into explaining some of the macro elements we see as explained by QM forces. A large part of the book is spent on symmetries and where a proton/nucleon's gluon binding mass comes from (a.k.a. ~95% of the mass we personally experience).
    
• The Higgs Boson and Beyond (Great Courses lecture)
  
  • Great lecture done by Sean Carroll around the time the Higgs boson's discovery was announced. It's a good combination of what role the Higgs plays in particle physics, why it's important and what's next. Also spends a little bit of time discussing how colliders like the LHC work.
    
• Mysteries of Modern Physics: Time (Great Courses lecture)
  
  • Not really heavy on QM at all, however I think it does best to do this lecture after having a bit of the physics under your belt first. The odd nature of time symmetry in the fundamental forces and what that means with regards to our understanding of time as we experience it is more impactful with the additional knowledge (but, like I said, not absolutely required).
    
• Deep Down Things: The Breathtaking Beauty of Particle Physics
  
  • This is not a mathematical approach like "A Most Incomprehensible Thing" are but it's subject matter is more advanced and the resulting math (at least) an order of magnitude harder (so it's a good thing it's skipped). This is a "high level deep dive" (whatever that means) into QFT though and so discussion of pure abstract math is a huge focus. Lie groups, spontaneous symmetry breaking, internal symmetry spaces etc. are covered.
    
• The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory
  
  • This is your desert after working through everything above. Had to include something about string theory here. Not a technical book at all but best to be familiar with QM concepts before diving in.
    
    Blending the line between pop-sci and mathematical (these books are not meant to be read and put away but instead read, re-read and pondered):
    
    
• A Most Incomprehensible Thing: Intro to GR
  
  • Sorry, this is GR specific and nothing to do with QM directly. However I think it's a great book acting as an introduction. Definitely don't go audible/kindle. Get the hard copy. Lots of equations. Tensor calculus, Lorentz transforms, Einstein field equations, etc. While it isn't a rigorous textbook it is, at it's core, a mathematics based description not analogies. Falls apart at the end, after all, it can't be rigorous and accessible at the same time, but still well worth the read.
    
• The Theoretical Minimum: What You Need to Know to Start Doing Physics
  
  • Not QM at all. However it is a great introduction to using math as a tool for describing our reality and since it's using it to describe classical mechanics you get to employ all of your classical intuition that you've worked on your entire life. This means you can focus on the idea of using math as a descriptive tool and not as a tool to inform your intuition. Which then would lead us to...
    
• Quantum Mechanics: The Theoretical Minimum
  
  • Great introduction that uses math in a descriptive way AND to inform our intuition.
    
• The Road to Reality: A Complete Guide to the Laws of the Universe
  
  • Incredible book. I think the best way to describe this book is a massive guidebook. You probably won't be able to get through each of the topics based solely on the information presented in the book but the book gives you the tools and knowledge to ask the right questions (which, frankly, as anybody familiar with the topic knows, is actually the hardest part). You're going to be knocking your head against a brick wall plenty with this book. But that's ok, the feeling when the brick wall finally succumbs to your repeated headbutts makes it all worth while.

> somebody knows a book about quantum field theory that is actually mathematically rigorous

I'm not sure that this really exists. You could maybe try Peter Woit's notes, but I wouldn't stick to a mathematician's take. I've never read Steven Weinberg, but I would trust him over pretty much anyone else. In any case, you may be underestimating the difficulty of physics even given a mathematics and physics background. Consider giving Sakurai or possibly Ballentine a thorough read before delving into quantum field theory. Asher Peres has a great book too. Chances are, you haven't really considered what, mathematically, the momentum and energy operators are actually doing. Respectively, they are generators of the groups of spatial translations/rotations (depending on if you are considering linear or angular momentum) or of time translation. This is pretty important to understand clearly, and I think it's worth appreciating the physical intuition before delving too deeply into the math involved.

One of my favourite books is Matrix Analysis, by Rajendra Bhatia. I think it's a crying shame that most (all?) undergraduate curricula do not cover the calculus of matrices (as opposed to the algebra of matrices). I think it's the logical conclusion of the sequence Single Variable Calculus --> Multivariable Calculus --> Vector Calculus. In particular, one should be aware that smooth functions of a diagonalizable matrix are equivalent up to a basis change to a smooth function of the eigenvalues of that matrix. This is a consequence of the Cayley-Hamilton theorem. But then you have to worry about the nastiness of errors in specifying either matrix elements or eigenvalues. There are lots of thorny but fascinating issues to consider here. This is, to me, the real foundation of quantum mechanics. All the junk about observables needs to be appreciated in context of the ability of measurement devices to respond to the eigenvalues of a Hamiltonian.

I think it's better to keep a focussed and small list of things to read. If you have some kind of electronic reading device, you'd be better advised to put PDFs of good books/notes/articles rather than carrying a bunch of paper. But if you're in Mozambique and therefore unlikely to have reliable power or internet (never been, so I could be wrong), I think you are better advised to pick one book and work through it diligently. I'd strongly recommend Hartshorne's Algebraic Geometry for this, but that's a pretty herculean effort. Algebraic Geometry is nice, though, because it requires every aspect of mathematical thought and is beautiful to boot.

A suggestion that is not so directly related to the ones you have given: Donald Knuth's The Art of Computer Programming. It could be the most important book of the twentieth century.

> The bra-ket notation is literally just a way of notating linear algebra. The math doesn't change because of how you write it down.

You've obviously never taken a quantum mechanics class. It's taught as one or the other. I'm not arguing it's different, hence why I said the bra-ket "notation". It's simply the way chemists and physicists prefer to represent the schrodinger equation because it makes their math look better for their most commonly used applications.

I present to you, a perfect example.

This here is a book generally used by chemists when being taught quantum mechanics.

https://www.amazon.com/Physical-Chemistry-Molecular-Donald-McQuarrie/dp/0935702997

And now here is a book generally used by physicists when being taught the same thing.

https://www.amazon.com/Principles-Quantum-Mechanics-R-Shankar-ebook/dp/B000SEIXA2

Do you see how one book works almost exclusively in the linear algebra space while the other works almost exclusively using bra-ket notation? It's a choice, made by professors. Yes, you can learn both, it's not hard. This is why I know you've never taken a quantum mechanics class because this is made extraordinarily clear to everybody in the class. "These two things teach you the same stuff but in different ways. We choose to use this way."

> As for physical chemistry defining how everything works, how much particle physics do you do as a physical chemist?

Well considering I'm a spectroscopist, and a mechanist, quite a bit actually. And sure, I'm sure particle theory absolutely can explain pretty much everything.... in the longest most roundabout way possible. I wasn't aware, however, that the interactions of quarks (other than the electron....) came into play for the typical, everyday chemical reactions that occur constantly. In fact, are there not very few reactions that humans can achieve that actually have enough energy to split a proton or neutron into their constituent parts? I'm pretty sure that once the big bang cooled down everything pretty much settled into the subatomic particles we know and love today. So I mean, unless you plan on replicating the types of heat seen in the big bang.... that level of detail is... well... superfluous. Sure, it MAY be useful in SOME nuclear reactions, but even then, not always. If particle theory explained everything, why is it not used to explain everything? Go on.... explain. I'm waiting.

Also I find it funny that you assume that we didn't learn about subatomic particles smaller than the proton and the neutron. We simply know that they aren't really that useful for most normal situations. In theory? Sure. In reality? No. We're chemists, not theorists. We get shit done.

> Edit: it's also worth noting that bra-ket notation is typically introduced at the undergraduate level of quantum mechanics.

Congratulations! You've discovered the meaning of the word "introduced!"

>1. Is Michio's statement an oversimplifying status of string theory really represents the current status?

All of Kaku's statements about anything are gross oversimplifications.

Strings have really opened up and branched in recent years. A sector of string theorists does phenomenology and attempts to reconstruct the SM in string models, and is concerned with the landscape, swampland, stability (nonperturbative and perturbative), hierarchies, see-saws and all that. But there's much more string theory beyond phenomenology. There's the question of the nature of emergence of spacetime - you know string theory is quantum gravity, but how exactly? What is there to learn about quantum gravity from strings? Also, the complete microscopic description of string theory is lacking, so what is string theory is still unkown. And what is M-theory? How does it work? And then there's holography, AdS/CFT, top-down, bottom-up, applications to QCD, condensed matter. And then black hole thermodynamics, information paradox and the connection between entanglement and geometry. Or the nature of the mathematics of string dynamics, such as the complex geometry of the perturbation series worldsheets or of the Calabi-Yaus in compactifications, exceptional symmetries such as E_8 or the monster group, all sorts of wacky stuff. And string cosmology!

All of these are valid and interesting branches to investigate. Paradoxically, being a Theory of Everything is just a tiny portion of string theory.

>2. If 1. is true, why haven't people tried to use complexity theory/protein folding/order parameter/landscape theory in order to reduce dimensionality of String theory such that we will remain with only one or few possible universes?

Hahaha, man, I don't think I can communicate just how much machinery and work has been poured over this problem - mostly because it's such an incredibly vast subject I have no hope of knowing everything about it. It's a really, really hard problem. Mostly because all of the questions above about how string theory exactly works beyond the perturbative regime are in part unanswered. And in part also because there is sometimes simply a brutally large amount of mindless calculations to do. The strategy is nowadays to try and find nontrivial conditions that effective theories need to satisfy to be stable, and use that to shave significant volume from the landscape and into the swampland. But still, every even vaguely good idea is well accepted, if it turns out to help. So, if you want to apply any idea from other fields to help shaving this sheep, I am not going to discourage you. Study some string pheno (I'll add a ref) and see if you get any lightbulbs.

>3. Are there any recommendation of good resources to deeply learn String theory/ToE stuff? (Review articles/Papers/ Lectures/book/UFO like sources)?

I like this book very much.

Understand though that a working knowledge of currently accepted high-energy physics is a prerequisite, so the standard model, its interactions, symmetries, spontaneous breaking and anomalies, RG group and hierarchies. Most subnuclear / fundamental interactions courses cover that, but I can send you a ref if you need a specific one. Also I would read up on standard Grand Unification models as a bridge, just if you have a personal interest; there is this beautiful review by John Baez which focuses on the mathematics and rep theory of embedding the standard model in a GUT (something that certain surfers should have taken a look at). But you might also be interested in physical aspects such as anomalies, proton decay, neutrino physics, topological defects (monopoles, cosmic strings, domain walls), and stuff.

Wow, do you go to some school where mathochism is cool? This is not a junior-level course in my academic worldview. It was not too too long ago that linear algebra was almost exclusively a graduate course. It was pushed down to the undergraduate level because of its extreme usefulness in ODEs and DSP, among other things. Undergraduates did not get that much smarter, instead the curriculum for linear algebra just got that much more streamlined. Your prof is either ignorant of or doesn't care about that evolution. If this is supposed to be a "regular" class, then you might voice a complaint to the chairperson of the department. Junior level courses usually are the introduction to mathematical rigor, not the launchpad for the study of Lie Algebras or other specialized areas. However if you are in an honors class or a hardcore mathematics school, you'll just have to strap in and enjoy the ride.

So here's some rope. All my references are old because I am old(ish). However, you can probably do better with keyword searches in Wikipedia and WolframAlpha based on your lecture notes. Do something like a mind map of the connections. The only thing you are missing online will be problems.

Go to your library and get Linear Algebra and Its Applications. I learned from an earlier edition of the book, but I can't imagine it getting worse. The people who hate the book are the ones who didn't do the exercises. If you stick with it, it is very cool and things start to build and just make sense. Strang is an excellent, excellent expositor, but you have to be a big picture person. He also tells you exactly what the core of the book is, The Fundamental Theorem of Linear Algebra. Grok that and linear algebra is your oyster, e.g., Gram-Schmidt will seem like an obvious thing. (And wouldn't you know, a reference on that Wikipedia page is to a paper by Strang on just that(pdf).)

If you can put up with older notation, you will find a lot in the famous book by Halmos, Finite Dimensional Vector Spaces.

A lot of this carries through to graduate algebra and functional analysis, so find whatever texts your graduate courses require and check their indices. From the above it sounds like your prof is trying to hit all the connections to other areas.

This next book will probably not help you, but it is just crazy enough to make me think you may find some of your professor's thoughts hidden there, Mathematical Physics by Geroch. You don't have time to learn category theory, but his exposition ends up at the spectral theorem, I seem to recall. Seeing another presentation of those powerful theorems might be illuminating. (It's a beautiful book, but I've never heard of it being used in a class.)

If you don't have MATLAB, get a (free?/cheap?) student edition and play with it for "real" examples of what you are doing. Going through the Theorem-Proof process never worked for me with things like linear algebra: Seeing how you can pull things apart and put them back together is what makes the power of linear algebra come alive and gives you some motivation.

The last piece of advice is not a guarantee, but has always worked for me when in a draconian course: Drill yourself on your old tests and quizzes and homework. When everyone is failing and the final comes around, chances are good (for various reasons, including pity and laziness) that the earlier exams are almost exactly recapitulated. Use your prof's office hours to go over the subtleties of the exam problems. If you are engaged with the material, the chances are good that he will extend the scope of discussion and pull in examples from the current lectures. That's a very handy insight to have.

If the notes of your class do make it online, please think of linking it back here. I'm curious as to how deep this course is since it is pretty wide.

For math you're going to need to know calculus, differential equations (partial and ordinary), and linear algebra.

For calculus, you're going to start with learning about differentiating and limits and whatnot. Then you're going to learn about integrating and series. Series is going to seem a little useless at first, but make sure you don't just skim it, because it becomes very important for physics. Once you learn integration, and integration techniques, you're going to want to go learn multi-variable calculus and vector calculus. Personally, this was the hardest thing for me to learn and I still have problems with it.

While you're learning calculus you can do some lower level physics. I personally liked Halliday, Resnik, and Walker, but I've also heard Giancoli is good. These will give you the basic, idealized world physics understandings, and not too much calculus is involved. You will go through mechanics, electromagnetism, thermodynamics, and "modern physics". You're going to go through these subjects again, but don't skip this part of the process, as you will need the grounding for later.

So, now you have the first two years of a physics degree done, it's time for the big boy stuff (that is the thing that separates the physicists from the engineers). You could get a differential equations and linear algebra books, and I highly suggest you do, but you could skip that and learn it from a physics reference book. Boaz will teach you the linear and the diffe q's you will need to know, along with almost every other post-calculus class math concept you will need for physics. I've also heard that Arfken, Weber, and Harris is a good reference book, but I have personally never used it, and I dont' know if it teaches linear and diffe q's. These are pretty much must-haves though, as they go through things like fourier series and calculus of variations (and a lot of other techniques), which are extremely important to know for what is about to come to you in the next paragraph.

Now that you have a solid mathematical basis, you can get deeper into what you learned in Halliday, Resnik, and Walker, or Giancoli, or whatever you used to get you basis down. You're going to do mechanics, E&M, Thermodynamis/Statistical Analysis, and quantum mechanics again! (yippee). These books will go way deeper into theses subjects, and need a lot more rigorous math. They take that you already know the lower-division stuff for granted, so they don't really teach those all that much. They're tough, very tough. Obvioulsy there are other texts you can go to, but these are the one I am most familiar with.

A few notes. These are just the core classes, anybody going through a physics program will also do labs, research, programming, astro, chemistry, biology, engineering, advanced math, and/or a variety of different things to supplement their degree. There a very few physicists that I know who took the exact same route/class.

These books all have practice problems. Do them. You don't learn physics by reading, you learn by doing. You don't have to do every problem, but you should do a fair amount. This means the theory questions and the math heavy questions. Your theory means nothing without the math to back it up.

Lastly, physics is very demanding. In my experience, most physics students have to pretty much dedicate almost all their time to the craft. This is with instructors, ta's, and tutors helping us along the way. When I say all their time, I mean up until at least midnight (often later) studying/doing work. I commend you on wanting to self-teach yourself, but if you want to learn physics, get into a classroom at your local junior college and start there (I think you'll need a half year of calculus though before you can start doing physics). Some of the concepts are hard (very hard) to understand properly, and the internet stops being very useful very quickly. Having an expert to guide you helps a lot.

Good luck on your journey!

I just want to point out one thing that everyone seems to be glossing over: when people say that you'll need to review classical mechanics, they aren't talking only about Newtonian Mechanics. The standard treatment of Quantum Mechanics draws heavily from an alternative formulation of classical mechanics known as Hamiltonian Mechanics that I'm willing to bet you didn't cover in your physics education. This field is a bit of a beast in its own right (one of those that can pretty much get as complicated/mathematically taxing as you let it) and it certainly isn't necessary to become an expert in order to understand quantum mechanics. I'm at a bit of a loss to recommend a good textbook for an introduction to this subject, though. I used Taylor in my first course on the subject, but I don't really like that book. Goldstein is a wonderful book and widely considered to be the bible of classical mechanics, but can be a bit of a struggle.

Also, your math education may stand you in better stead than you think. Quantum mechanics done (IMHO) right is a very algebraic beast with all the nasty integrals saved for the end. You're certainly better off than someone with a background only in calculus. If you know calculus in 3 dimensions along with linear algebra, I'd say find a place to get a feel for Hamiltonian mechanics and dive right in to Griffiths or Shankar. (I've never read Shankar, so I can't speak to its quality directly, but I've heard only good things. Griffiths is quite understandable, though, and not at all terse.) If you find that you want a bit more detail on some of the topics in math that are glossed over in those treatments (like properties of Hilbert Space) I'd recommend asking r/math for a recommendation for a functional analysis textbook. (Warning:functional analysis is a bit of a mindfuck. I'd recommend taking these results on faith unless you're really curious.) You might also look into Eisberg and Resnick if you want a more historical/experimentally motivated treatment.

All in all, I think its doable. It is my firm belief that anyone can understand quantum mechanics (at least to the extent that anyone understands quantum mechanics) provided they put in the effort. It will be a fair amount of effort though. Above all, DO THE PROBLEMS! You can't actually learn physics without applying it. Also, you should be warned that no matter how deep you delve into the subject, there's always farther to go. That's the wonderful thing about physics: you can never know it all. There just comes a point where the questions you ask are current research questions.

Good Luck!

That's perfect then, don't let me stop you :). When you're ready for the real stuff, the standard books on quantum mechanics are (in roughly increasing order of sophistication)

• Griffiths (the standard first course, and maybe the best one)
  
• Cohen-Tannoudji (another good one, similar to Griffiths and a bit more thorough)
  
• Shankar (sometimes used as a first course, sometimes used as graduate text; unless you are really good at linear algebra, you'd get more out of starting with the first two books instead of Shankar)
  
  By the time you get to Shankar, you'll also need some classical mechanics. The best text, especially for self-learning, is [Taylor's Classical Mechanics.] (http://www.amazon.com/Classical-Mechanics-John-R-Taylor/dp/189138922X/ref=sr_1_1?s=books&ie=UTF8&qid=1372650839&sr=1-1&keywords=classical+mechanics)
  
  
  Those books will technically have all the math you need to solve the end-of-chapter problems, but a proper source will make your life easier and your understanding better. It's enough to use any one of
  
  
• Paul's Free Online Notes (the stuff after calculus, but without some of the specialized ways physicists use the material)
  
• Boas (the standard, focuses on problem-solving recipes)
  
• Nearing (very similar to Boas, but free and online!)
  
• Little Hassani (Boas done right, with all the recipes plus real explanations of the math behind them; after my math methods class taught from Boas, I immediately sold Boas and bought this with no regrets)
  
  When you have a good handle on that, and you really want to learn the language used by researchers like Dr. Greene, check out
  
  
• Sakurai (the standard graduate QM book; any of the other three QM texts will prepare you for this one, and this one will prepare you for your PhD qualifying exams)
  
• Big Hassani(this isn't just the tools used in theoretical physics, it's the content of mathematical physics. This is one of two math-for-physics books that I keep at my desk when I do my research, and the other is Little Hassani)
  
• Peskin and Schroeder (the standard book on quantum field theory, the relativistic quantum theory of particles and fields; either Sakurai or Shankar will prepare you for this)
  
  Aside from the above, the most relevant free online sources at this level are
  
  
• Khan Academy
  
• Leonard Susskind's Modern Physics lectures
  
• MIT's Open CourseWare

And will remain in a super-position state until OP collapses the probability function by observing the screen!

As a sidenote, anyone interested in quantum theory should check out Quantum Enigma by Rosenblum/Kuttner, a general summary of the contradictory ideas that drive quantum physics. I've read others such as Beginner's Guide to Quantum Physics and The Mathematical Principles of Quantum Mechanics, but found that the Rosenblum/ Kuttner is by far the most clear and easiest to understand without a physics/ math background. Another great one is Einstein and the Quantum: The Quest of the Valiant Swabian, which gives a great account of the historical beginnings of quantum physics as a scientific field (focusing on Einstein of course). Very well-written, andectotal, and an awesome read for anyone interested in the history of science.

Come join /r/quantum! We need more posts!

The Feynman Lectures are a perfect introduction to physics from high school level all the way up to degree level.

A good understanding of maths is essential to more advanced physics and there is an excellent textbook written by two extremely qualified headmaster's called The Language Of Physics: A Foundation for University Study which is what's recommended to first year University students and poses questions at the end of each chapter.

If you're looking for something a little less intimidating, then the A Very Short Introduction series have a perfect range of short (and cheap!) books on Physics: [Quantum Theory]
(https://www.amazon.co.uk/gp/product/0192802526/ref=pd_sim_14_4?ie=UTF8&psc=1&refRID=9A3MSV2XSQRYF880MYP6), Relativity, Particle Physics, Cosmology, Nuclear Physics, Black Holes, Thermodynamics, Astrophysics, Light and Magnetism. These are great little books that don't blow your head off!

Physics is an extremely interesting subject to read around and I wish you the best with it :)

My 2c: if you're already familiar with Python, check out sympy. The tutorials are actually quite good!

http://docs.sympy.org/latest/tutorial/

I'm one of these weird software hippys, so I'm not going to lie and say I didn't suggest it because it's free and open-source. However, it really is getting to the point where it's quite stable and usable with the addition that the language it's associated with is indeed a programming language designed to be programmed in by real programmers. I shan't say much on the issue, but there are problems with Maple and Mathematica as programming languages.

The problems with Sympy are that it is not yet so well documented. In particular, there aren't really any complete 'textbooks' as such on the market with more complete examples. For my part, I started as a Maple user and now I use sympy. In addition, there are certain features yet to be implemented. For example, last I checked, the ode solver does not know about the 'classical' differential equations (Hermite, Bessel, Legendre and friends) and often gives garbage when asked to solve them.

I will also point out that the 'giants' Maple (with which I am more familiar) and Mathematica are indeed excellent, robust and well-tested computer algebra solutions. If that's all you're really after, you can't really go wrong. I'm not so familiar with Sagemath, but for stability, useability and quality of documentation, it sits somewhere between Mathematica/Maple and Sympy.

If you needed a book for Maple, the following is the best I've found in the context of theoretical physics:

https://www.amazon.co.uk/d/Books/Physics-Computer-Algebra-Resource-Mathematical-Methods-Textbook/3527406409/ref=sr_1_3?ie=UTF8&qid=1484612452&sr=8-3&keywords=maple+physics

edit: I'd also like to add that while Maple and Mathematica are excellent prototype languages in the context of computational physics and chemistry (and are even quite fast for final implementation for some purposes!), if you're looking to write large-scale simulations, I'd think about learning C, C++ and Fortran and polishing your Python as a prototype language, not least because all are far better documented and have far larger communities.

Just a note, if you go into physics for nuclear fusion, you will probably be studying plasma physics so I've listed some useful books. Another route for supporting nuclear fusion research is material science because the plasma-wall interactions are important for fusion energy. Another approach is condensed matter research.. specifically into superconductors in my uncreative mind (but I'm sure there are other ways to support fusion work) because you need to confine that shit. There are probably a lot more ways to support fusion research so don't this as the final word.

-----
Just a general popular science kind of book:

An Indispensable Truth: How Fusion Power Can Save the Planet by F F Chen

Good introductions to plasma physics that don't completely skimp out on maths:

Introduction to Plasma Physics by R J Goldston and P H Rutherford

Statistical Plasma Physics by S Ichimaru

The equivalent to Jackson for all those mf'ing plasma waves:

Waves in Plasmas by T H Stix

Check out some books about string theory, it does make a case for solving the disconnect (as you without any doubt know).

Now the thing is, string theory solves things in a really intuitive and elegant way, which - being physicist myself - truly makes me want to believe it all checks out!

Depending on where you currently are in your education (and how much you like a tough challenge :)) you may want to have a look at this(undergrad) or this (graduate, pretty dense) book - they are both pretty great!

Yep, many physicists subscribe to the "shut-up-and-calculate" school of thought.

OP - although physics can't really address some of your specific questions, the mathematical link between the quantum and classical regimes is quite clear: if one considers the limit of a quantum system with a very large number of particles (e.g., every single atom in a rock), then the properties of the set of particles will be more clustered around their average values. These average values (expectation values) exactly match the classical predictions for that set of particles.

There's a great chapter that goes through all the math pretty clearly in R. Shankar's Principles of Quantum Mechanics.

You might want to take a look at the following book:

An Introduction to Computer Simulation Methods: Applications To Physical Systems

https://www.amazon.co.uk/dp/1974427471/

It’s a textbook at the undergraduate level. The choice of programming language is debatable but the breadth and depth of the material covered are pretty great. You’ll learn a great deal of computational physics from it.

Wow, thanks for the Reddit gold, that's awesome! It's been my pleasure to have the discussion with you. As for a good textbook, I have a few suggestions. For a pretty good broad look at optics from both classical and quantum points of view, give Saleh and Teich a look. For purely quantum stuff, my undergrad textbook was by Griffiths, which I enjoyed quite a bit, though I recall the math being a bit daunting when I took the course. Another book I've read that I liked quite a bit was by Shankar. I felt it was a bit more accessible. Finally, if you want quantum mechanics from the source, Dirac is a bit of a standard. It's elegant, but can be a bit tough.

If your goal is to understand basic concepts without the math, then a highschool physics book would most likely be the best place to start, as the highest math used is usually Algebra/Pre-calc.

That being said, without at least a calculus background it's hard to grasp some of the concepts beyond basic kinematics. Wikipedia might get you somewhere so it's a good place to start, but it could also lead you through a rabbit hole to pages upon pages of background.

I'd say if you want to tackle more advanced physics concepts then you need at least some background in math, so I'd try Mathematical Methods in the Physical Sciences by Mary Boas, a book that explains the physics and math somewhat side by side, or The Road to Reality: A Complete Guide to the Laws of the Universe by Roger Penrose. Neither is a light read, if you don't have a head for math don't even try Penrose as he uses arguments that assume a reasonable mathematical background. The Boas book is technically a mathematics textbook, so you would do well to supplement it with a College Physics textbook (I used one by Tipler in my university courses).

Amazon Links Below:
Penrose: http://www.amazon.com/Road-Reality-Complete-Guide-Universe/dp/0679776311/ref=sr_1_1?s=books&ie=UTF8&qid=1404248577&sr=1-1&keywords=the+road+to+reality+roger+penrose

Boas: http://www.amazon.co.uk/Mathematical-Methods-Physical-Sciences-Mary/dp/0471365807/ref=sr_1_1?s=books&ie=UTF8&qid=1404248599&sr=1-1&keywords=boas

Tipler: http://www.amazon.co.uk/Physics-Scientists-Engineers-Modern/dp/1429202653/ref=pd_sim_sbs_b_1?ie=UTF8&refRID=1NX3QE9FG7XGKWQ15NQ4

Hope this helps, good luck!

With a year of physics you can start to work through this book https://www.amazon.com/Computational-Physics-Mark-Newman/dp/1480145513/ref=sr_1_3?s=books&ie=UTF8&qid=1499909731&sr=1-3&keywords=physics+python

I learned Python with it and I really enjoyed it. I tried the different free online courses that ran you through the basics but I lost interest. What kept me going was seeing immediately how Python can be used to solve various physics problems. I would say you can easily get through this book this summer before graduate school.

Edit: Forgot to mention that there are a few chapters online for free if you want to look through them before buying the book. With your background the problems will be really straight forward, but I would say that would help you focus more on learning Python, but still doing physics (which makes it more fun).

What I would suggest:

Introduction to Modern Optics by Fowles. It's short and to the point.

The Oxford Solid State Basics by Simon. The author also has lectures posted on his website that are fantastic. Additionally, Roald Hoffmann has a series of papers that introduce solid state concepts that are useful for chemists. They're very worthwhile reads. Here, here, and here.

Computational Physics by Newman. I find this really easy to read and understand. A lot of people around here recommend it.

What are you trying to be? Have one book just slightly deeper than Greene's book, or actually learn theoretical physics to say become a theoretical physicist or at least understand it?

If the former, it will be difficult as there's a lot of things that might be tacitly assumed that you know about more basic physics. However, a very good intro to Quantum Mechanics is Shankar. I'd also look into Foster and Nightingale's relativity book for a brief introduction to special (read Appendix A first) and general relativity. Maybe after both try A. Zee intro to QFT if you want to learn more about QFT. If you want to learn about phenomenological particle physics, say look at Perkins. Also it may help to have a book on mathematical physics, such as Boas or Arfken. (Arfken is the more advanced book, but has less examples). Also it may help to get a basic modern physics book that has very little math, though I can't think of any good ones.

If the latter than you will have to learn a lot. Here's advice from Nobel Laureate theoretical physicist Gerardus t'Hooft.

You need to know dynamics in Lagrangian and Hamiltonian formalisms. Get more solid on waves, and electromagnetism. Then you need to do quantum mechanics up through and including scattering, perturbation theory, and Fermi's golden rule (Shankar is a fantastic quantum text that will get you there in modern notation as well as introduce you to Feynman path integrals). Then you can start tackling quantum field theory. Sredniki's book is free online, but it's presentation is very nonstandard. It will, however, take you all the way to and past the standard model, which is nice. Lahiri and Pal is nice but short (with all the problems associated with that), Zee is good, and Peskin is more or less standard. Any of them will take you up through electroweak symmetry breaking and the Higgs mechanism.

And of course all the math along the way. Differential equations (ordinary and partial) and complex analysis need to be hit hard.

Not sure about the other topics, but if you really want to learn about the science of time dilation, I would recommend checking out Brian Greene's free courses on Special Relativity (either the conceptual one or the really math-centered one) and perhaps A Most Incomprehensible Thing by Peter Collier (a math-centered book that can potentially take the layman from high school mathematics to the equations of General Relativity).

I thought of some books suggestions. If you're going all in, go to the library and find a book on vector calculus. You're going to need it if you don't already know spherical coordinates, divergence, gradient, and curl. Try this one if your library has it. Lots of good books on this though. Just look for vector calculus.

Griffiths has a good intro to E&M. I'm sure you can find an old copy on a bookshelf. Doesn't need to be the new one.

Shankar has a quantum book written for an upper level undergrad. The first chapter does an excellent job explaining the basic math behind quantum mechanics .

This is the standard QM text for a large sector of undergraduates. It's what I used and it's very good as an introductory text. I can highly recommend it. Another excellent text is Shankar's book. Some prefer it as it's perhaps more in depth and comprehensive. It's been a while since I've read any QM books, but the last one I read that I quite liked was Bohm's Quntum Theory, though it's dense and a little out of date.

i recommend the following books by shankar (who is also the author of a well known quantum mechanics book). the books are accompanied by the open yale courses on physics.

• fundamentals of physics: mechanics, relativity, and thermodynamics
  
  
• fundamentals of physics ii: electromagnetism, optics, and quantum mechanics
  
  if you have a solid background in mathematics with just a little physics, i think these would do nicely. they're modern and not overly bloated. you can gain a little from each of the core areas to have the knowledge you'd need to proceed.

It’s gonna sounds ironic, but I tell people to start with String Theory for Dummies:

https://www.amazon.com/String-Theory-Dummies-Andrew-Zimmerman/dp/047046724X

It talks a little about String Theory, but really most of the book is catching you up on the developments in modern physics so you have a mental framework to grok what gave rise to quantum in the first place

I sent a copy to /u/TFnarcon9 - he can tell you what he thinks (if he’s read it yet)

Also keep in mind something called the “Ultraviolet Catastrophe”:

https://en.m.wikipedia.org/wiki/Ultraviolet_catastrophe

That’s kinda what kicked off the quantum thing. Combined with Einstein’s photoelectric effect

There’s a whole swath to learning various context of physics, and then there’s the actual application of math. To honestly learn how to solve problems in quantum, you need to learn about eigenstates and eigenvalues, for which I recommend Khan’s videos in linear algebra:

https://www.khanacademy.org/math/linear-algebra/alternate-bases/eigen-everything/v/linear-algebra-finding-eigenvectors-and-eigenspaces-example

But there’s not really a “Okay now I know quantum physics” thing

My professor always said, “There’s One ☝️ physics.”

There’s just different contexts, and we have found different tools / theories / models for those various contexts that make grokking, predicting, and modeling easier

Hi, what I am doing is plotting the probability of an electron in ay given position and seeing how changing its energy, spin projection and magnetic orientation.

The other side of my project, which I did not discuss there, was investigating quantum harmonic oscillators.

The books that I learned this from were A Cavendish Quantum Mechanics Primer and the language of physics; I think the former is better than the latter.

Also, try to read through the comments on that thread and come back with any questions. I am currently doing a writeup for the whole thing, so once I have that finished I'll see if I can share it.

I've found Riley, Hobson and Bence and Boas to be really good applied textbooks. The Bence is more of an introduction and the Boas goes more in-depth. If your morals are less than scrupulous then you can easily find a pdf of both online for free

Griffith's quantum is OK. Not bad, but all in all it lacks a bit of depth. I recommend Shankar's book. It covers a lot more of the basic formalism that lays the foundation for quantum mechanics. I would say it falls into an odd area in that it cover more material than is needed for an undergrad class, but not quite enough for a grad class. Nonetheless, it is an excellent introduction, especially for self-study.

Principles of Quantum Mechanics, Shankar

In my opinion, easier to follow than Griffiths. It explains principles better. Covers bra-ket, integral and matrix forms throughout. Many fewer gaps in getting from point a to point b than Griffiths. For someone studying on their own, the fewer gaps the better.

As an addition:

While Griffith's book on quantum mechanics is fantastic, I really enjoyed Claude Cohen-Tannoudji's book: https://www.amazon.com/Quantum-Mechanics-Vol-Claude-Cohen-Tannoudji/dp/047116433X/

If you have the mathematical foundation, you will find it a very thorough introduction to quantum mechanics.

There are LOTS of interesting physical phenomena you can simulate.

If you can find this book (even an earlier edition) in your school’s library, you’ll get a good idea of how vast the fields of computational physics and computer simulations are:

An Introduction to Computer Simulation Methods: Applications To Physical Systems

https://www.amazon.co.uk/dp/1974427471/

The latest edition uses java rather than python but, still, it will open your eyes to a LOT of very cool applications.

Physics for Poets is a pretty easy read, and covers most relevant topics.

I recall Physics for Poets being pretty good.

My undergrad waves course used this and I found it pretty clear. https://www.amazon.com/Waves-Oscillations-Prelude-Quantum-Mechanics/dp/019539349X

Can anyone recommend books for computational physics?
I have some experience with programming but would like a book that additionally teaches a new language.
Any thoughts on:
https://www.amazon.com/gp/product/1480145513/ref=ox_sc_mini_detail?ie=UTF8&psc=1&smid=A2MZMG0JK9LPC2
https://www.amazon.com/dp/3527413154/ref=pd_luc_rh_bxgy_01_03_t_ttl_lh?_encoding=UTF8&psc=1

I'm finishing up the tail end of an undergraduate introduction to computational physics using this book. I'm really interested in the a lot of this stuff, could anyone recommend a text book that we be a step up from this?

One book that is both inexpensive and generally well received is Peter Collier's A Most Incomprehensible Thing: Notes Towards a Very Gentle Introduction to the Mathematics of Relativity.

Shankar is a good quantum book, for an advanced undergraduate. Townsend is more elementary (for an intermediate undergraduate). And of course there's Feynman lectures volume 3 for something yet more basic. (And this one's at least free.)

If you have a have a math background up to ODEs and PDEs, this book is great. https://www.amazon.com/Most-Incomprehensible-Thing-Introduction-Mathematics/dp/0957389450/ref=sr_1_1?s=books&ie=UTF8&qid=1475030510&sr=1-1&keywords=a+most+incomprehensible+thing

Griffiths > Eisberg > Sakurai > Zee > Peskin

Peres and Ballentine offer a more quantum information oriented approach, read em after Griffiths.

Shankar before Sakurai, after Griffiths.



In that order. Your best bet though, is to find the appropriate section in the nearest university library, spend a day or two looking at books and choose whatever looks most interesting/accessible. Be warned, it seems that everyone and their cat has a book published on quantum mechanics with funky diagrams on the cover these days. A lot of them are legitimate, but make little to no effort to ensure your understanding or pose creative problems.

Brush up on mathematical methods for physics. Learn Linear Algebra, Ordinary and Partial Differential Equations, Multivariable Calculus, Complex Analysis, and Tensor Analysis. A good book would be this: http://www.amazon.com/Mathematical-Methods-Physical-Sciences-Mary/dp/0471198269/ref=ntt_at_ep_dpi_1

Classical Mechanics: http://www.amazon.com/Mechanics-Third-Course-Theoretical-Physics/dp/0750628960/ref=sr_1_7?s=books&ie=UTF8&qid=1291625026&sr=1-7

E&M: http://www.amazon.com/Electromagnetic-Fields-Roald-K-Wangsness/dp/0471811866/ref=ntt_at_ep_dpi_1
or http://www.amazon.com/Introduction-Electrodynamics-3rd-David-Griffiths/dp/013805326X/ref=sr_1_1?s=books&ie=UTF8&qid=1291625100&sr=1-1

Statistical Mechanics: http://www.amazon.com/Fundamentals-Statistical-Thermal-Physics-Frederick/dp/1577666127/ref=sr_1_1?ie=UTF8&s=books&qid=1291625184&sr=1-1

Quantum Mechanics: http://www.amazon.com/Principles-Quantum-Mechanics-R-Shankar/dp/0306447908/ref=sr_1_4?s=books&ie=UTF8&qid=1291625261&sr=1-4

Walter Smith's Waves and Oscillations: An prelude to quantum mechanics is ideal if you are looking for something at the undergraduate level.

Here are some Math-related books on my shelves:

• OUP - The Language of Physics (Loan; do NOT buy a copy of this. But do have one read through this. Only high-school maths necessary, and gives you a nice overview.)
  
• Kreyszig - Advanced Engineering Mathematics (I highly recommend this book. Read the first few chapters of each section for now (e.g: Ch 1, 2, 6, 7, 8, 11, 13, 15, 19, 24) since those are likely to be what you'll be covering first.)
  
• Stephenson - Mathematical Methods of Science Students (Others recommend this. I have a copy, but it's not something to pick up and read through. Quite dense and compact, more of a reference book that happens to include exercise problems with answers.)
  
• Kasdin & Paley - Engineering Dynamics (Not a maths book, but hey, if you've done Physics in HS, you pretty much get the grounding to do this stuff, especially after brushing up on ODEs. Take a look through Appendices A-C first, and use Kreyszig if you don't understand the maths.)
  
  I haven't read every introductory book in existence (neither have I had to), so these aren't necessarily the best ones.

Well, I don't mind reading a few equations. My former institute would be ashamed of me if I couldn't even do that.

Let me clarify. By "non-mathematical", I don't want to read pages and pages of derivations, justifications, and proofs. I want to get a book with excellent qualitative descriptions of the particles, their functions, the stories behind their discoveries, experimental descriptions of the verification of each one, and how they interact with each other.

I've been looking at these few titles:

http://www.amazon.com/Standard-Model-Primer-Cliff-Burgess/dp/0521860369

http://www.amazon.com/Introduction-Standard-Model-Particle-Physics/dp/0521852498/ref=sr_1_2?s=books&ie=UTF8&qid=1342797161&sr=1-2&keywords=standard+model

http://www.amazon.com/Introduction-Elementary-Particles-David-Griffiths/dp/3527406018/ref=pd_bxgy_b_text_b


Do you any experience with these few?

The typical introductory quantum mechanics book is probably Griffiths, but if you already have an introductory grasp of basic quantum physics, linear algebra, and calculus, I instead recommend,

Quantum Mechanics Vol 1, Claude Cohen-Tannoudji

My own quantum mechanics education has been sparse and poorly taught, but I have seen a lot of the quantum mechanics books and can say that Cohen-Tannoudji has a two-volume set which is second to none:

https://www.amazon.com/Quantum-Mechanics-Vol-Claude-Cohen-Tannoudji/dp/047116433X

If you aren't specifically reading Sakurai for course preparation, I emphatically recommend this approach instead. It starts from axioms and derives things in an understandable way.

I really like ballentine's and shankar's text books

http://amzn.com/9814578584

http://amzn.com/0306447908

You may be interested in Mathematical Physics by Paul Geroch.

I think this book by Collier. should match up relatively^haha well with what you're looking for.

A good, fairly self contained book on QM, is the one by Shankar. This is a textbook intended for serious study, but it also introduces most of the math it uses. That is not a substitute for studying the math separately, but might do in a pinch.

I can recommend the book, but its only close to ELI5....

http://www.amazon.com/String-Theory-Dummies-Andrew-Zimmerman/dp/047046724X/ref=sr_1_1?ie=UTF8&qid=1395379544&sr=8-1&keywords=string+theory+for+dummies

"Computational Physics" by Mark Newman

https://www.amazon.com/Computational-Physics-Mark-Newman/dp/1480145513


There are sample chapters available if you want to try before you buy
http://www-personal.umich.edu/~mejn/cp/chapters.html

This book sort of similar:

http://www.amazon.com/Physics-Poets-Robert-March/dp/0072472170

Caveat Emptor:
http://www.insidehighered.com/views/2006/04/13/morley

sprichst du von echten Fachbüchern oder von allgemeinverständlicher Literatur?

Fachbücher: String theorie: barton Zwiebach
https://www.amazon.de/First-Course-String-Theory/dp/0521880327

QM: Cohen Tannoudji
https://www.amazon.de/Quantum-Mechanics-Vol-Claude-Cohen-Tannoudji/dp/047116433X/ref=sr_1_1?s=books-intl-de&ie=UTF8&qid=1465804024&sr=1-1&keywords=cohen+tannoudji

http://www.amazon.com/Waves-Oscillations-Prelude-Quantum-Mechanics/dp/019539349X

Se quiser aprender recomendo como introdução :

https://www.amazon.com/Principles-Quantum-Mechanics-2nd-Shankar/dp/0306447908

Agora se só precisa de algum tópico especifico seja mais claro...

Theoretical particle physics: all three massive volumes of Weinberg's The Quantum Theory of Fields.

Every professor I know in the field has this on their bookshelf. People talk about "taking a year" to do a detailed reading of this book. It's so nitty gritty that I don't think any course in the world uses it, but you gotta know it.

I get that, but I was referring to Principles of Quantum Mechanics,
R Shankar

I used this during my undergrad:

https://www.amazon.com/Computational-Physics-2nd-Nicholas-Giordano/dp/0131469908/

There's also this, that seems highly reviewed:

https://www.amazon.com/Computational-Physics-Mark-Newman/dp/1480145513/

The Giordano book probably requires a basic physics/math background (caluclus, linear algebra, classical mechanics, electricity/magnetism, basic quantum). Dunno about the other.

On the real model the same interactions appear (the potential is always the mexican hat). The real model is actually very simple when you get used to the transformation properties of the fields. This http://www.amazon.com/Standard-Model-Primer-Cliff-Burgess/dp/0521860369 has a very simple approach!

“Computational Physics” by Mark Newman is a first class book to learn from. I was taught from it in my undergraduate career and I have repeatedly gone back to it for reference. The language is python so that might be a turn off for some people.

>Pinterest for Dummies.

Redundant.

And this one, String Theory for Dummies, sort of cracks me up. If you're a dummy, maybe, just maybe, you shouldn't be trying to tackle String Theory.

String Theory for Dummies is probably good for you. It talks about string theory as if you were an idiot, so it should be right up your alley.

This should keep you busy, but I can suggest books in other areas if you want.

Math books:
Algebra: http://www.amazon.com/Algebra-I-M-Gelfand/dp/0817636773/ref=sr_1_1?ie=UTF8&s=books&qid=1251516690&sr=8
Calc: http://www.amazon.com/Calculus-4th-Michael-Spivak/dp/0914098918/ref=sr_1_1?s=books&ie=UTF8&qid=1356152827&sr=1-1&keywords=spivak+calculus
Calc: http://www.amazon.com/Linear-Algebra-Dover-Books-Mathematics/dp/048663518X
Linear algebra: http://www.amazon.com/Linear-Algebra-Modern-Introduction-CD-ROM/dp/0534998453/ref=sr_1_4?ie=UTF8&s=books&qid=1255703167&sr=8-4
Linear algebra: http://www.amazon.com/Linear-Algebra-Dover-Mathematics-ebook/dp/B00A73IXRC/ref=zg_bs_158739011_2

Beginning physics:
http://www.amazon.com/Feynman-Lectures-Physics-boxed-set/dp/0465023827

Advanced stuff, if you make it through the beginning books:
E&M: http://www.amazon.com/Introduction-Electrodynamics-Edition-David-Griffiths/dp/0321856562/ref=sr_1_1?ie=UTF8&qid=1375653392&sr=8-1&keywords=griffiths+electrodynamics
Mechanics: http://www.amazon.com/Classical-Dynamics-Particles-Systems-Thornton/dp/0534408966/ref=sr_1_1?ie=UTF8&qid=1375653415&sr=8-1&keywords=marion+thornton
Quantum: http://www.amazon.com/Principles-Quantum-Mechanics-2nd-Edition/dp/0306447908/ref=sr_1_1?ie=UTF8&qid=1375653438&sr=8-1&keywords=shankar

Cosmology -- these are both low level and low math, and you can probably handle them now:
http://www.amazon.com/Spacetime-Physics-Edwin-F-Taylor/dp/0716723271
http://www.amazon.com/The-First-Three-Minutes-Universe/dp/0465024378/ref=sr_1_1?ie=UTF8&qid=1356155850&sr=8-1&keywords=the+first+three+minutes

http://www.amazon.com/Principles-Quantum-Mechanics-R-Shankar/dp/0306447908/ref=pd_sim_b_2 this one or this http://www.amazon.com/Introductory-Quantum-Mechanics-4th-Edition/dp/0805387145/ref=sr_1_fkmr0_1?ie=UTF8&qid=1346229545&sr=8-1-fkmr0&keywords=Liboff+and+Bransden ?

I got feynman's books but the structure annoyed me a bit, he just seems to talk about everything in a random order :P

stop reading shit.

if you want to read about quantum mechanics, i would suggest this for a beginner.

The two intro texts you'll see all the time for quantum are Shankar and Griffiths. I would recommend Shankar of those two since Griffiths skips a bunch of critical mathematical definitions. However, even Shankar may be a bit above your current math level. I don't know what 6th form or A-level means but quantum can get into ugly math and weird notation very quickly.