University of North Carolina at Asheville
Subject Listing - Physics/Astronomy
Advisor: Dr. Michael J. Ruiz
Friday, Oral Session 6, Presentation 1, Robinson Hall 217
NUMERICAL ANALYSIS OF THE INVERSE TRAPEZOID POTENTIAL
Examination of one-dimensional potential wells has a long history in quantum mechanics. For this project, an inverse trapezoidal potential well is constructed for use in the one-dimensional Schrödinger equation. This potential energy function alternates between constant and linear regions. Since this potential cannot be solved analytically due to the diagonal regions, numerical methods are utilized to compute the solutions. An eighth-order Runge-Kutta method is used to approximate solutions to this second order differential equation. The algorithm, written in Java, identifies the energy of correct solutions by testing their normalizability. This algorithm is used to compute the bound state solutions over the family of trapezoidal systems. Data is collected for the first six bound states on regular intervals of angle and slope. Graphing this data shows an interesting evolution of the energy states as the trapezoid becomes steeper. The analytic solution to the limiting case of the finite square well is used to verify this data, and provides a good comparison to the behaviors of this system.
Advisor: Dr. Michael J. Ruiz, Professor, Department of Physics, University of North Carolina at Asheville, Asheville, NC