What are the necessary steps to study advanced Q MECH on your own?

[AKSHAT2012]

currently i am joining IIT for an ee btech(b e) degree. i am very passionate for continuing my studies in physics after it, but still i want to study Q mech,G R,on my own
here is what i am familiar with as of now.
MATHS
CALCULUS -TILL pde (variable separable),ODE -double order .
vector calculus till stokes threorem(only the preliminaries)

PHYSICS
Q mech till application to hydrogen atom.
some basic statistical mech.
S R till simultaniety, velocity addition.

now i want to go to advanced q mech, start G R.

please tell 1.if this math is sufficient 2. what books are best 3.what more (and in how much detail i have to learn more).4. what exactly comes in advanced q mech 5.anything u would like to add.
i will be greately indebted.
(thanks in advance) -akshat

 

[Matterwave]

By "advanced Q-mech" you mean...the quantum mechanics leading up to quantum field theory? E.g., the Dirac Equation, EM field quantization, second quantization, and so forth?

 

[AKSHAT2012]

that is exactly my question i don't know what i have to study to get deeper into quantum mechanics,as i said i only know the basics (say schrodingers eqn ,priciple ,orbital magnetic quantum nos.,eigenfunctions, expectation values,harmonic oscillators ...)to say i have read significant portion of arthur beiser.
what to read after is it elementary particles?is it treatment to many electron atoms?...

 

[cragar]

Check out Principles of Quantum Mechanics by R. Shankar. And start reading it. Skip around or whatever . Its really thorough .

 

[AKSHAT2012]

Thanks.
and can you tell me the higher maths that is required apart for other topics like general relativity and ,quantum mechanics, of course.

 

[WannabeNewton]

GR has quite a slew of mathematical knowledge required that one can always pick up while learning it, I'll try to name whatever comes to my head: topology and following that differential geometry, linear algebra, some group theory would help for advanced treatments (if you ever study the spinor formalism), and tensor analysis. Again you learn a lot of the differential geometry and tensor analysis while reading introductory texts and they are to an extent one and the same subjects at that level but studying some topology would make things much more coherent. I don't think I need to mention calculus as you already know much of what is needed and it should be a given anyways if you are learning these things on your own. If you study Shankar's QM text like cragar suggested then you won't have any trouble at all going to QFT; learning some group theory would definitely help you in the future here as well. For GR I suggest you use either "A First Course in General Relativity" -Schutz and/or "Gravity, An Introduction To Einstein's Relativity" - Hartle.

 

[AKSHAT2012]

thanks to all