Finite Element Analysis of the Schroedinger Equation
Avtar S. Sehra
TL;DR
This paper explores the application of finite element methods to solve the Schrödinger equation, comparing different numerical time evolution techniques for quantum mechanical problems.
Contribution
It introduces finite element analysis to quantum mechanics and evaluates three numerical methods for solving the Schrödinger equation.
Findings
Finite element method can be applied to quantum problems.
Crank-Nicolson, continuous, and discontinuous methods are compared.
Results demonstrate effectiveness of finite element approaches in quantum simulations.
Abstract
The purpose of this work is to test the application of the finite element method to quantum mechanical problems, in particular for solving the Schroedinger equation. We begin with an overview of quantum mechanics, and standard numerical techniques. We then give an introduction to finite element analysis using the diffusion equation as an example. Three numerical time evolution methods are considered: the (tried and tested) Crank-Nicolson method, the continuous space-time method, and the discontinuous space-time method.
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Taxonomy
TopicsContact Mechanics and Variational Inequalities · Numerical methods in engineering · Advanced Numerical Methods in Computational Mathematics