Degree Year
2017
Document Type
Thesis - Open Access
Degree Name
Bachelor of Arts
Department
Physics and Astronomy
Advisor(s)
Daniel F. Styer
Keywords
BEM, Degeneracy, Symmetry, Quantum, Mechanics
Abstract
The relationship between degeneracy and symmetry in quantum mechanics is explored using two dimensional infinite potential wells with boundaries |x|^n + |y|^n = an for n = 2, whose limiting cases are circular (n = 2) and square (n ¿ 8) well. Analytic solutions for the circular and square cases are derived from separation of variables. Boundary element method (BEM) is a numerical method that solves PDEs using boundary conditions. The BEM is used to solve potential well problems. The method is first tested by comparing numerical solutions with analytic solutions for the circular and square wells. For the ground state of the circular well, the error as a function of the number of discretization points N decreased like 1/N^2. As the potential well changed shape from circle to square, energy eigenvalues and degeneracies are tracked. Energy levels split (when degeneracies are lifted), merge, and cross.
Repository Citation
Lee, Dahyeon, "From the Circle to the Square: Symmetry and Degeneracy in Quantum Mechanics" (2017). Honors Papers. 188.
https://digitalcommons.oberlin.edu/honors/188
