On One Implementation of the Numerov Method for the One-Dimensional Stationary Schrödinger Equation

We present accurate numerical results for the one-dimensional stationary Schrödinger equation in the case of three quantum problems: quantum harmonic oscillator, radial Schrödinger equation for a Hydrogen atom, and a particle penetration through the potential barrier. All of them were solved by the...

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Bibliographic Details
Published in:	Physics of particles and nuclei letters Vol. 18; no. 2; pp. 153 - 159
Main Authors:	Purevkhuu, M., Korobov, V. I.
Format:	Journal Article
Language:	English
Published:	Moscow Pleiades Publishing 01-03-2021 Springer Nature B.V
Subjects:	Boundary value problems Eigenvalues Harmonic oscillators Numerical analysis Numerical methods Particle and Nuclear Physics Physics Physics and Astronomy Physics of Elementary Particles and Atomic Nuclei. Theory Potential barriers Schrodinger equation Wave functions the Numerov method potential barrier eigenproblem Harmonic oscillator
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Summary:	We present accurate numerical results for the one-dimensional stationary Schrödinger equation in the case of three quantum problems: quantum harmonic oscillator, radial Schrödinger equation for a Hydrogen atom, and a particle penetration through the potential barrier. All of them were solved by the Numerov method with high accuracy and we plot their wave functions using the results of numerical calculations. Furthermore, we offer accurate numerical methods for solving boundary value problems, eigenvalue problems, matrix elimination.
ISSN:	1547-4771 1531-8567
DOI:	10.1134/S154747712102014X