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Solving the Schrödinger Equation for Bound States with Mathematica 3.0

Wen-Fa Lu
Organization: Yonsei University
Department: Institute of Physics and Applied Physics
F. Schöberl
Journal / Anthology

International Journal of Modern Physics
Year: 1999
Volume: 10
Issue: 4
Page range: 607-619

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.

*Science > Physics > Quantum Physics