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Solving the one-dimensional time-independent Schrödinger equation with high accuracy: The LagrangeMesh Mathematica® package

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  • J. C. del Valle

    (Institute of Mathematics, Faculty of Mathematics, Physics and Informatics, University of Gdańsk, 80-308, Gdańsk, Poland)

Abstract

In order to find the spectrum associated with the one-dimensional Schrödinger equation, we discuss the Lagrange Mesh Method (LMM) and its numerical implementation. 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 and highly accurate 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 the potential function and the interval on which it is defined; and (ii) the accuracy in calculations and final results is controllable by the user. Due to its high accuracy and simple usage, the package may be used as a research and educational tool. As illustration, a highly accurate spectrum of some relevant quantum systems is obtained by employing the commands that the package offers.

Suggested Citation

  • J. C. del Valle, 2024. "Solving the one-dimensional time-independent Schrödinger equation with high accuracy: The LagrangeMesh Mathematica® package," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 35(01), pages 1-32, January.
    • Handle: RePEc:wsi:ijmpcx:v:35:y:2024:i:01:n:s0129183124500116
    DOI: 10.1142/S0129183124500116
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