This repository houses my comprehensive solutions for an independent study course on Symmetry and Quantum Mechanics, focusing on the intricate algebra underlying Quantum Mechanics. It's designed to showcase my proficiency in advanced Quantum Mechanics and algebra to academic and research-oriented audiences.
This was an independent study led by Scott Corry, Professor at Math Department of Lawrence University. He wrote a book on this topic. We studied this book thoroughly and solved problems from within the text, so please refer to it when viewing my solutions.
Key topics and concepts explored in this course include:
- Complex Vector Spaces: Fundamental understanding and application of complex vector spaces in Quantum Mechanics.
- Lie Algebra: In-depth exploration of Lie algebra and its critical role in the theoretical framework of Quantum Mechanics.
- Group Isomorphisms: Detailed study of isomorphisms between various groups relevant to Quantum Mechanics.
- Group Actions: Analysis of group actions and their implications in quantum systems.
- Invariant Subspaces of Heisenberg Group: Examination of invariant subspaces within the context of the Heisenberg group.
- Spin Angular Momentum Operators: Computation and interpretation of expectation values of spin angular momentum operators in physical space.
- PDF Solutions: This repository primarily features a PDF of my detailed solutions to a range of problems, reflecting my analytical approach to understanding and applying the principles of Quantum Mechanics and symmetry.
The material in this repository is particularly relevant for:
- Advanced Quantum Mechanics Students: Offering a resource for those seeking a deeper understanding of the algebraic underpinnings of Quantum Mechanics.