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

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Discussion Overview

The discussion centers on the steps necessary for self-studying advanced quantum mechanics (Q-mech) and general relativity (GR). Participants explore the mathematical prerequisites, recommended resources, and the scope of advanced topics in these fields.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Homework-related

Main Points Raised

  • One participant outlines their current knowledge in mathematics and physics, expressing a desire to study advanced Q-mech and GR independently.
  • Another participant seeks clarification on what constitutes "advanced Q-mech," suggesting it may include topics leading to quantum field theory, such as the Dirac Equation and EM field quantization.
  • A participant indicates uncertainty about the next steps in their studies, questioning whether to focus on elementary particles or many-electron atoms after mastering the basics of quantum mechanics.
  • Recommendations for study materials include "Principles of Quantum Mechanics" by R. Shankar, noted for its thoroughness.
  • Discussion on the mathematical knowledge required for GR includes topology, differential geometry, linear algebra, group theory, and tensor analysis, with the suggestion that much of this can be learned concurrently with studying GR.
  • It is mentioned that calculus is a foundational requirement, which the original poster already possesses.
  • For GR, suggested texts include "A First Course in General Relativity" by Schutz and "Gravity, An Introduction To Einstein's Relativity" by Hartle.

Areas of Agreement / Disagreement

Participants express varying levels of agreement on the recommended resources and mathematical prerequisites, but there is no consensus on the exact path to follow for advanced Q-mech or the specific topics to prioritize.

Contextual Notes

Participants acknowledge the need for additional mathematical knowledge but do not specify the depth or breadth required for each topic. The discussion reflects a range of perspectives on the necessary steps and resources for self-study.

AKSHAT2012
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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
 
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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?
 
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?...
 
Check out Principles of Quantum Mechanics by R. Shankar. And start reading it. Skip around or whatever . Its really thorough .
 
Thanks.
and can you tell me the higher maths that is required apart for other topics like general relativity and ,quantum mechanics, of course.
 
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.
 
thanks to all
 

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