Solving the One-Dimensional Time-Independent Schr\"odinger Equation with High Accuracy: The LagrangeMesh Mathematica Package
Abstract
In order to find the spectrum associated with the one-dimensional Schr\"oodinger equation, we discuss the Lagrange Mesh method (LMM) and its numerical implementation for bound states. After presenting a general overview of the theory behind the LMM, we introduce the LagrangeMesh package: the numerical implementation of the LMM in Mathematica. Using few lines of code, the package enables a quick home-computer computation of the spectrum and provides a practical tool to study a large class of systems in quantum mechanics. The main properties of the package are (i) the input is basically the potential function and the interval on which is defined; and (ii) the accuracy in calculations and final results is controllable by the user. As illustration, a highly accurate spectrum of some relevant quantum systems is obtained by employing the commands that the package offers. In fact, the present work can be regarded as a user guide based on worked examples.
Keywords
Cite
@article{arxiv.2208.14340,
title = {Solving the One-Dimensional Time-Independent Schr\"odinger Equation with High Accuracy: The LagrangeMesh Mathematica Package},
author = {J. C. del Valle},
journal= {arXiv preprint arXiv:2208.14340},
year = {2023}
}
Comments
File LagrangeMesh.wl can be provided to the interested reader, just contact the author via email. Alternatively, it can be found at https://github.com/JuanCarlosdelValle/LagrangeMesh-Package