Matrix Numerov method for solving Schrödinger’s equation

Matrix Numerov method for solving Schrödinger’s equation

We recast the well-known Numerov method for solving Schrödinger’s equation into a representation of the kinetic energy operator on a discrete lattice. With just a few lines of code in a high-level programming environment such as mathematica, it is simple to calculate and plot accurate eigenvalues an...

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Bibliographic Details
Published in:American journal of physics Vol. 80; no. 11; pp. 1017 - 1019
Main Authors: Pillai, Mohandas, Goglio, Joshua, Walker, Thad G.
Format: Journal Article
Language:English
Published: Woodbury American Institute of Physics 01-11-2012
Subjects:
Algebra
Eigenvalues
Kinetics
Mathematical problems
Numerical analysis
Schrodinger equation
Online Access:Get full text
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Summary:We recast the well-known Numerov method for solving Schrödinger’s equation into a representation of the kinetic energy operator on a discrete lattice. With just a few lines of code in a high-level programming environment such as mathematica, it is simple to calculate and plot accurate eigenvalues and eigenvectors for a variety of potential problems. We illustrate the method by calculating high-accuracy solutions for the | x | potential.
ISSN:0002-9505
1943-2909
DOI:10.1119/1.4748813