Differential equations in Quantum Mechanics

[gomes.]

Studying a maths degree, going onto final year next year, am planning to do a 3rd year course in quantum mechanics.

I just want to ask, how much probability theory and differential equations are there in quantum mechanics? Someone said that ultimately quantum mechanics is about probability theory and differential equations, is that true? if so, in what areas of quantum mechanics?

Cheers

 

[G01]

A full length course in probability theory will be overkill for what you need in quantum mechanics.

PDE's are important( solving the Shrodinger equation), however, if you know the separation of variables method, you'll be fine.

Group and Representation Theory is also important, but for a 3rd year undergraduate course on QM, it probably won't be emphasized too much.

More important for undergraduate quantum mechanics, IMO, is linear algebra. Having a good understanding of vector spaces will help a lot with understanding Quantum Mechanics.

 

[A. Neumaier]

Studying a maths degree, going onto final year next year, am planning to do a 3rd year course in quantum mechanics.

I just want to ask, how much probability theory and differential equations are there in quantum mechanics? Someone said that ultimately quantum mechanics is about probability theory and differential equations, is that true? if so, in what areas of quantum mechanics?

Linear ordinary and partial differential equations with constant coefficients, to be solved by an exponential ansatz is a must - used in the Schroedinger equation from the very beginning. Probability theory looks quite different from the usual QM point of view than in math; so you don't need it at all for a first course in QM since quantum physicists explain it all in their terms.

 

[gomes.]

thanks for your help :)