Reddit mentions of A Modern Approach to Quantum Mechanics

Griffiths is the go-to for advanced undergraduate level texts, so you might consider his Introduction to Quantum Mechanics and Introduction to Particle Physics. I used Townsend's A Modern Approach to Quantum Mechanics to teach myself and I thought that was a pretty good book.

I'm not sure if you mean special or general relativity. For special, /u/Ragall's suggestion of Taylor is good but is aimed an more of an intermediate undergraduate; still worth checking out I think. I've heard Taylor (different Taylor) and Wheeler's Spacetime Physics is good but I don't know much more about it. For general relativity, I think Hartle's Gravity: An Introduction to Einstein's General Relativity and Carroll's Spacetime and Geometry: An Introduction to General Relativity are what you want to look for. Hartle is slightly lower level but both are close. Carroll is probably better if you want one book and want a bit more of the math.

Online resources are improving, and you might find luck in opencourseware type websites. I'm not too knowledgeable in these, and I think books, while expensive, are a great investment if you are planning to spend a long time in the field.

One note: teaching yourself is great, but a grad program will be concerned if it doesn't show up on a transcript. This being said, the big four in US institutions are Classical Mechanics, E&M, Thermodynamics/Stat Mech, and QM. You should have all four but you can sometimes get away with three. Expectations of other courses vary by school, which is why programs don't always expect things like GR, fluid mechanics, etc.

I hope that helps!

> I studied it for A-level (age 16-18 in the UK, but likely has more content than the American equivalent) and did some applied maths, but I'm pretty rusty.

You might want to start by studying classical mechanics and electrodynamics then.

• • 
    
    Anyway, as to your main question:
    
    Townsend, [A Modern Approach to Quantum Mechanics*](http://www.uscibooks.com/townsend3.htm) (amazon)
    
    This one starts more sensibly than most QM textbooks which try to (sorta) re-hash the historical development of the subject and are filled with problems and explanations with unnecessarily gnarly formulae.
    
    I think it gives a better idea of what quantum mechanics is about and how to think about it than e.g. Griffiths’s book.
    
    If you want something more introductory, it’s possible Townsend’s other book might suit you better – I haven’t looked at it though.

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.)

Thanks very much for the advice! We are using A Modern Approach to Quantum Mechanics by John S. Townsend.

Edit: Amazon Link

A Modern Approach to Quantum Mechanics By Townsend is the text that my class used. It's approachable and thorough, and requires only minimal prereq knowledge to get started (EM, Linear Algebra, some calculus, Complex numbers).