Thursday, 18 July 2019

resource recommendations - Linear algebra for quantum physics



A week ago I asked people on this site what mathematical background was needed for understanding Quantum Physics, and most of you mentioned Linear Algebra, so I decided to conduct a self-study of Linear Algebra. Of course, I'm just 1 week in, but I have some questions.




  1. How is this going to be applicable to quantum physics? I have learned about matrices (addition, subtraction, multiplication and inversion) and about how to solve multiple equations with 3 unknowns using matrices, and now I am starting to learn about vectors. I am just 1 week in, so this is probably not even the tip of the iceberg, but I want to know how this is going to help me.





  2. Also, say I master Linear Algebra in general in half a year (I'm in high school but I'm extremely fast with maths), what other 'types' of math would I need to self-study before being able to understand rudimentary quantum physics mathematically?





Answer



Quantum mechanics "lives" in a Hilbert space, and Hilbert space is "just" an infinite-dimensional vector space, so that the vectors are actually functions. Then the mathematics of quantum mechanics is pretty much "just" linear operators in the Hilbert space.



Quantum mechanics Linear algebra
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wave function vector
linear operator matrix

eigenstates eigenvectors
physical system Hilbert space
physical observable Hermitian matrix

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