Mathematics of Quantum Mechanics

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SUMMARY

Quantum mechanics requires a robust understanding of several mathematical concepts, including differential equations, complex analysis, linear algebra, probability theory, and functional analysis on Hilbert spaces. Key topics such as wave mechanics and matrix mechanics are essential, alongside integrals, Fourier series, and the theory of distributions. The recommended resource for a mathematically oriented treatment is "Quantum Mechanics" by Galindo and Pascual, published by Springer Verlag in 1990.

PREREQUISITES
  • Differential equations
  • Complex analysis
  • Linear algebra
  • Functional analysis on Hilbert spaces
NEXT STEPS
  • Study wave mechanics and matrix mechanics in detail
  • Explore probability theory applications in quantum mechanics
  • Learn about integrals and Fourier series in the context of quantum theory
  • Read "Quantum Mechanics" by Galindo and Pascual for a comprehensive understanding
USEFUL FOR

Students and professionals in physics, mathematicians, and anyone interested in the mathematical foundations of quantum mechanics.

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What form of mathematics does quantum theory require? Please, HELP!
 
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Differential equation, Complex analysis, and Linear algebra, etc.

Any way, try to search these two words: wave mechanics, matrix mechanics.
 
Thanks a lot!
 
Some probability theory and lots of integrals, including multiple integrals, Fourier series..
 
You need functional analysis on Hilbert spaces, including the theory of distributions. A nice more mathematically oriented modern treatment is

Galindo, A., and Pascual, P.: Quantum Mechanics, Springer Verlag, 1990, 2 Vols.
 
Hendrik, the G&P is the best book one could possibly reccomand. I fully endorse it.
 
OK I will try to issue a buncha books from my library.
Thanks again!
 

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