Procedure for studying advanced quantum mechanics.

[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

 

[R.Mesri]

1. Yes, your current math background is sufficient for studying advanced quantum mechanics and general relativity.2. For advanced quantum mechanics, a good book to start with is Griffiths' Introduction to Quantum Mechanics. This provides an excellent introduction to the foundational concepts of quantum mechanics. Other books that you may find useful are the Quantum Mechanics: Concepts and Applications by N. Zettili and the Quantum Mechanics by Eisberg and Resnick. For general relativity, a good book to start with is Schutz's A First Course in General Relativity. This provides a comprehensive overview of the key concepts and equations of general relativity. Another book that may be useful is Spacetime Physics by Taylor and Wheeler. 3. In addition to the topics you have already listed, you should also familiarize yourself with the various mathematical tools used in quantum mechanics and general relativity, such as tensors, linear algebra, and differential geometry. You should also read up on the various experiments that have been performed to verify the predictions of these theories, such as the double-slit experiment and the gravitational lensing experiment. 4. Advanced quantum mechanics covers topics such as the solutions of the Schrödinger equation, the density matrix formalism, the Heisenberg uncertainty principle, and the spin-orbit coupling effect. It also covers topics such as the WKB approximation and the variational method. 5. General relativity covers topics such as the Schwarzschild solution, the Kerr solution, the Friedmann-Lemaitre-Robertson-Walker metric, and the Raychaudhuri equation. It also covers topics such as the geodesic equation and the Einstein field equations. Finally, it is important to note that quantum mechanics and general relativity are two of the most difficult topics in physics and it is essential to have a solid foundation in mathematics and physics in order to understand them. Therefore, it is recommended that you take the time to read up on the relevant topics and gain a thorough understanding of the underlying concepts before attempting to tackle the more advanced topics.