Representation Theory Techniques in Quantum Mechanics -- Special Topics Course (Graduate) -- MATH 5750
This course built up concepts in Representation Theory from the base level using Abstract Algebra and Vector Space Analysis, while introducing elementary concepts in Quantum Mechanics. The idea was to learn to build and/or recognize isomorphisms between vector spaces so the student could then understand how to utilize representations of known sources to better understand a representation of the hydrogen atom within the context of the quantum realm. By the end of the course, each student group had the necessary tools to make use of representation theory in their future academic pursuits, but my research topic, in particular, was the capstone to the original course outline. In moving from the special orthogonal group in 3 dimensions -- or SO(3) -- through the quaternions to su(2) by isomorphism, my research constructed a method of studying the bound states of the hydrogen atom by studying the representation of the direct product of two copies of su(2).
