How Can Variational Calculus Enhance Your Understanding of Quantum Mechanics?

[aliaze1]

I am taking a Quantum Mechanics course this semester and the professor started off by showing us how Newtonian Mechanics lead to Lagrangian Mechanics, then Hamiltonian...etc...until we got to the Quantum Mechanical wave functions.

This was all done in a quantitative sense, using variational calculus. Does anyone know of any good mathematics/physics/mathematical physics textbook that goes into this type of detail for mechanics? I was looking into "Advanced Calculus" by Loomis, since Loomis' Calculus book was amazing, I imagine the Advanced book would be good too..

 

[nirax]

you have got a very good teacher. many times such personal viewpoints are impossible to find in any book. and taking lessons from classroom is the only way to get such personal viewpoints. so absorb it as much as you can. discuss with the person too. you will not get a chance later on.

 

[Landau]

I think you will like https://www.amazon.com/dp/0486650677/?tag=pfamazon01-20.
https://www.amazon.com/dp/0486630692/?tag=pfamazon01-20 talks about calculus of variations, including may applications.

 

[alexepascual]

Of course you'll need some calculus, but I also suggest you get a good understanding of linear algebra. You might also start looking at the Dirac notation (after you study a little linear algebra).
In older QM books you see states expressed in terms of wave functions with integrals, etc. and a lot of calculus. Newer books use more the Dirac notation, which is based on the linear algebra and the fact that you can represent functions in a "Hilbert space"
Books:
"Classical Mechanics" by Herbert Goldstein.
"Mathematical Methods for Physicsists" Arfken.
"Mathematical Methods in the Physical Sciences" is also good. But Arfken is a little more advanced I think. It wouldn't hurt having both.