Application of representation theory

Question

I often read that one can use representation theory in the field of quantum physics or for the analysis of symmetries in physics or chemistry. Unfortunately I couldn't find a concrete example for this. I would be very happy if someone could describe me a concrete application of linear representation theory of finite groups (modular and arbitrary theory over rings). Is this theory e.g. useful for the Schrödinger equation?

Answer 1

Your question seems to ask more for a reference. There are many good papers for this that I read through while looking at this for my undergraduate thesis. Here are a few good references to get you started at why the two are connected:

Representation Theory, Symmetry, and Quantum Mechanics

Quantum Mechanics and Representation Theory

and this which is not as related but easier to read.

Answer 2

I Googled representation theory in quantum mechanics and found:

• Quantum Field Theory and Representation Theory

To quote the source: In 1928 Weyl published a book called "Theory of Groups and Quantum Mechanics", which had alternate chapters of group theory and quantum mechanics.

I think that you will find the rest of the the source most enlightening.