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Hello Math Community,

Thank you for taking the time to read my question. It is much appreciated. I'm curious as to which branch of mathematics would help develop our understanding of quantum theory ( quantum mechanics, spatial orientation of electrons ......). I am an undergrad graduating soon with a math degree and wishes to transition to advanced math. But before that I want to spend a considerable amount of time exposing myself to advanced math. When it comes to quantum mechanics my intuition tells me maybe topology or differential geometry are involved. Please help me understand which general topics I should consider thank you.

shiff desta
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  • See this question, or this one at MSE. – Dietrich Burde May 15 '18 at 18:10
  • For undergraduate QM, linear algebra and differential equations (both ODE's, and preferably a little PDE's) are all that's necessary. For advanced QM, you move up to functional analysis and group theory (As Noah Schweber mentioned) to get a good handle on the math. You'll find that special functions are used extensively; you can sometimes get a good treatment of that in functional analysis - it certainly provides the right framework for understanding special functions. – Adrian Keister May 15 '18 at 18:14
  • The field of $\Bbb C^*$-algebra (which is a part of functional analysis) was developed specifically for its applications to quantum mechanics. – Arthur May 15 '18 at 18:29
  • Quantum Mechanics In Hilbert Space (and other books) by Eduard Prugoveski.... See him in Wikipedia – DanielWainfleet May 15 '18 at 19:04

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