Numerical Method for a Confined Atomic System

Clark, Deleonne, A. Sarsa, Ehme, Jeffry

Published Jul 1, 2015• 0 citations

Abstract

Quantum confinement is a relatively new subject matter in quantum mechanics. Quantum confinement traps the atom in a cavity whose dimensions are small enough to alter its properties. Some physicists have used the time-independent Schrodinger equation to obtain exact results for confinement problems. But this paper focuses on the dynamic of a hydrogen atom when it is moved from captivity. The goal of this project is to study and understand different methods used to predict solutions that cannot be obtained analytically which was done by relying on methods that approximates solutions. To do this, a differential equation with boundary conditions was manipulated with the computer programs C++ and Eclipse using Runge-Kutta, B-Splines, and the Schrodinger equation. While the Runge-Kutta method was utilized as a basis for the boundary problem, its simplicity was not viable for this research which contained so many complex variables. Instead, B-Splines were used to solve the time-dependent Schrodinger equation. B-Spline functions are designed to generalize polynomials for the purpose of approximating arbitrary functions. By taking the summation of the timeindependent Schrodinger equation, we obtained our desired results for the timedependent Schrodinger equation.

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