#### 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