Intermediate qm what should i know

[professor]

i eventually wish to learn all that i possibly can, though atm i have only recently bothered with qm much at all. I have a near complete as i can get understanding of Relativity, have read the original papers by lorentz, einstein, and the like...so if you wish to base any comments on that view of things you may. What i am most interested in is Mathmatical equations governing any sort of phenomena explainable by qm, especially thouse that contradict relativity. If you could point me in the right direction i would be most greatfull. (no need to explain basics of the uncertainty principle and the like, and do not worry if comples math is involved I am working on my tensor calc atm, but i don't believe qm is quite as advanced in that respect in comparison to relativity).

 

[dextercioby]

Trust me, the mathematics behind the General Theory of Relativity is far easier than the one involved in Quantum Mechanics and Quantum Field Theory...

Daniel.

 

[Kruger]

Elementary quantum mechanics is mostly based on the SCHRÖDINGER EQUATION. So you could take a look on this differential equation. Its fundamental. Then with this equation you should know something about "EIGENVALUES" and quantum mechanical "EXPECTATION VALUES" and "DEFIATIONS" and of course something about boulding "COMPLEX WAVE FUNCTIONS".

Well this is basic. If you want to connect QM with SR you can make your introduction via the "DIRAC EQUATION" (this is a common intro) and QFT with the quantization of the harmonic oscillator and the electromagnetic field.

If you can all that you've a fundamental knowledge. You can then calculate quite easy some simpel interactions between particle. and make an approach to calculate for example "Fermis Golden Rule", i.e. easy scattering processes (what you should know then is PERTURBATION THEORY).

So this a short review.

 

[professor]

thank you greatly kruger, and on the note of dexter, what sort of math is then involved in qm...i would assume some sort of linear algebra would be the basis.

 

[McQueen]

What i am most interested in is Mathmatical equations governing any sort of phenomena explainable by qm, especially thouse that contradict relativity. If you could point me in the right direction i would be most greatfull.

Quantum Mechanics by I V Savelev , "Fundamentals Of Theoretical Physics" is a great start.

 

[George Jones]

thank you greatly kruger, and on the note of dexter, what sort of math is then involved in qm...i would assume some sort of linear algebra would be the basis.

Only dextercioby can speak for himself, but he might mean that if the mathematics of quantum theory is considered by the standards of mathematics, then stuff like the spectral theorem for unbounded self-adjoint operators, worrying about (possibly dense) domains of operators and commutators, rigged hilbert spaces, etc. This is functional analysis - linear algebra extended to an infinite number of dimensions and combined with analysis.

And that's just for non-relativistic quantum mechanics.

For relativistic quantum theory including the standard model, stuff like clifford algebras and spinors, operator-valued distributions, and the representation theory of Lie algebras and Lie groups is needed.

Regards,
George

 

[fdarkangel]

Heisenberg stated quantum mechanics with matrix calculus, which was shown to be equivalent to Schrödinger's with partial differentials. partial differentions seem to be quite more adorable to physicsts, i guess.