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From The Circle To The Square: Symmetry And Degeneracy In Quantum Mechanics, Dahyeon Lee
From The Circle To The Square: Symmetry And Degeneracy In Quantum Mechanics, Dahyeon Lee
Honors Papers
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 …