Using the Finite Element Method for Solving the Schrödinger Equation
Open Access
Author:
Sofo, Ignacio
Area of Honors:
Mathematics
Degree:
Bachelor of Science
Document Type:
Thesis
Thesis Supervisors:
Victor Nistor, Thesis Supervisor Victor Nistor, Thesis Supervisor Svetlana Katok, Thesis Honors Advisor
Keywords:
Finite Element Method error analysis
Abstract:
The Finite Elements Method was rst presented in an address to the American Mathematical Society by Richard L. Courant. The method was presented as part of a two-page appendix where he showed how piecewise-linear approximations on a set of elements could be used to solve partial di erential
equations. The purpose of this paper is to look at solutions of a 1-dimensional Schrodinger equation using the Finite Element Method. By looking at the eigenvalues of the Schrodinger operator and applying the method, we can transform it into a matrix eigenvalue problem. In particular, this paper will be focusing on the two main sources of error that accompany this numerical method: the size of the elements, and the overall size of our mesh.
