SOLVING THE SCHRÖDINGER EQUATION FOR BOUND STATES WITH MATHEMATICA 3.0

Wolfgang Lucha () and Franz F. Schöberl
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Wolfgang Lucha: Institut für Hochenergiephysik, Österreichische Akademie der Wissenschaften, Nikolsdorfergasse 18, A-1050 Wien, Austria
Franz F. Schöberl: Institut für Theoretische Physik, Universität Wien, Boltzmanngasse 5, A-1090 Wien, Austria

International Journal of Modern Physics C (IJMPC), 1999, vol. 10, issue 04, 607-619

Abstract: Using Mathematica 3.0, the Schrödinger equation for bound states is solved. The method of solution is based on a numerical integration procedure together with convexity arguments and the nodal theorem for wave functions. The interaction potential has to be spherically symmetric. The solving procedure is simply defined as some Mathematica function. The output is the energy eigenvalue and the reduced wave function, which is provided as an interpolated function (and can thus be used for the calculation of, e.g., moments by using any Mathematica built-in function) as well as plotted automatically. The corresponding program schroedinger.nb can be obtained from franz.schoeberl@univie.ac.at.

Keywords: Schroedinger equation; Bound state; Energy eigenvalue; Wave function; Numerical solution (search for similar items in EconPapers)
Date: 1999
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DOI: 10.1142/S0129183199000450

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