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Thesis.pdf (1.43 MB)
ETD Abstract Container
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From the Circle to the Square: Symmetry and Degeneracy in Quantum Mechanics
Author Info
Lee, Dahyeon
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=oberlin1497568215606295
Abstract Details
Year and Degree
2017, BA, Oberlin College, Physics and Astronomy.
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.
Committee
Daniel F. Styer (Advisor)
Pages
38 p.
Subject Headings
Physics
;
Quantum Physics
Keywords
BEM
;
degeneracy
;
symmetry
;
quantum
;
mechanics
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Citations
Lee, D. (2017).
From the Circle to the Square: Symmetry and Degeneracy in Quantum Mechanics
[Undergraduate thesis, Oberlin College]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=oberlin1497568215606295
APA Style (7th edition)
Lee, Dahyeon.
From the Circle to the Square: Symmetry and Degeneracy in Quantum Mechanics.
2017. Oberlin College, Undergraduate thesis.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=oberlin1497568215606295.
MLA Style (8th edition)
Lee, Dahyeon. "From the Circle to the Square: Symmetry and Degeneracy in Quantum Mechanics." Undergraduate thesis, Oberlin College, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=oberlin1497568215606295
Chicago Manual of Style (17th edition)
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Document number:
oberlin1497568215606295
Download Count:
5,000
Copyright Info
© 2017, all rights reserved.
This open access ETD is published by Oberlin College Honors Theses and OhioLINK.