Intermediate qm what should i know

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In summary, Daniel is interested in learning more about quantum mechanics and mathematics behind it. He has a basic understanding of the basics, but is more interested in those equations that contradict relativity. He would like to find a guide to help him learn more.
  • #1
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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 origional 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).
 
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Trust me, the mathematics behind the General Theory of Relativity is far easier than the one involved in Quantum Mechanics and Quantum Field Theory...:rolleyes:

Daniel.
 
  • #3
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.
 
  • #4
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.
 
  • #5
Professor said:
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.
 
  • #6
professor said:
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
 
  • #7
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.
 

1. What is intermediate quantum mechanics?

Intermediate quantum mechanics is a subfield of physics that focuses on the study of quantum phenomena at an intermediate level between basic and advanced quantum mechanics. It involves the application of mathematical tools and concepts to understand the behavior of particles at the atomic and molecular level.

2. What are the key concepts I should know in intermediate quantum mechanics?

Some of the key concepts in intermediate quantum mechanics include wave-particle duality, quantum states and operators, uncertainty principle, measurement and observables, and quantum entanglement. It is also important to have a solid understanding of linear algebra and calculus.

3. How is intermediate quantum mechanics different from basic quantum mechanics?

Intermediate quantum mechanics builds upon the fundamental principles and concepts of basic quantum mechanics, but it delves deeper into the mathematical formalism and applies it to more complex systems and phenomena. It also introduces new concepts such as perturbation theory and scattering theory.

4. What are some real-world applications of intermediate quantum mechanics?

Intermediate quantum mechanics has numerous applications in modern technology, such as in the development of quantum computers, quantum cryptography, and quantum sensors. It also plays a crucial role in understanding the behavior of atoms and molecules in chemical reactions, as well as in the study of materials at the nanoscale.

5. What are some resources I can use to learn more about intermediate quantum mechanics?

There are many textbooks, online courses, and lecture notes available for learning intermediate quantum mechanics. Some recommended resources include "Intermediate Quantum Mechanics" by Hans A. Bethe and Richard Friedberg, "Quantum Mechanics: Concepts and Applications" by Nouredine Zettili, and the MIT OpenCourseWare course "Intermediate Quantum Mechanics" by Allan Adams.

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