Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Chemical Education

Numerical solution of the one-dimensional Schrödinger equation

Uldis Blukis, J. M. Howell

Published Mar 1, 1983• 15 citations
Publisher

Abstract

  1. These authors discuss some advantages of the numerical approach to introductory quantum mechanics, present some specifics of using Noumerov's formula, and present some the results.
DOI
10.1021/ed060p207

Related papers

Numerical errors resulting from finite-difference approximation in computations of a one-dimensional Schrödinger equation with the Trotter formula

Norio Inui

Computer Physics Communications•Jul 12, 2007•1 citation

8 Numerical Solution of the Schrödinger Equation

Princeton University Press eBooks•Dec 31, 2008•0 citations

Computer Solutions to a Realistic “One-Dimensional” Schrödinger Equation

Jay Sharon Bolemon

An important technique for teaching introductory wave mechanics is provided by the numerical calculation of stationary state solutions of the Schrödinger equation. Realistic problems in wave mechanics that do not require sophisticated computer techniques are very valuable for the instruction of undergraduates. In the central-field model for atoms, the calculation of electron states reduces to the solution of a one-dimensional differential equation whose numerical solutions are no more difficult to obtain than those for a finite square well. A method used by our students is discussed in this paper for the calculation of the electron wavefunctions in a central-field potential. By working this problem, students obtain meaningful results that give them insight into the theory of atomic structure. Results of their experience are included, and possibilities of extending this example are discussed.

American Journal of Physics•Oct 1, 1972•13 citations

More on Numerical Solutions to Simple One-Dimensional Schrödinger Equations

Charles K. Manka

American Journal of Physics•Oct 1, 1972•1 citation

Time Dependent Schrödinger Equations with Vector Potentials - Numerical Calculations and Visualizations -

Hiroshi Natori, Tomo Munehisa

We study algorithm to calculate the time dependent Schrödinger equation numerically and to visualize the results. We extend the product formula by the Trotter-Suzuki decomposition to cases of Hamiltonians with vector potentials. This method is unconditionally stable and it can be used for a time dependent Hamiltonian so that one can apply it to various problems without any difficulty. After examining numerical errors for time evolutions of one dimensional wave packets, we present the errors under a constant magnetic field. Also we discuss a cyclotron motion in quantum mechanics, where an advantage for the unconditional stability is demonstrated. In order to visualize the results we make animations of the time evolutions, where the phase of the wave function is represented by colors and its absolute value is shown by brightness. Here we suggest a new way to represent a complex number by colors.

Journal of the Physical Society of Japan•Feb 15, 1997•9 citations

9. One-dimensional Schrödinger equation and its solutions

De Gruyter eBooks•Aug 4, 2014•0 citations
An important technique for teaching introductory wave mechanics is provided by the numerical calculation of stationary state solutions of the Schrödinger equation. Realistic problems in wave mechanics that do not require sophisticated computer techniques are very valuable for the instruction of undergraduates. In the central-field model for atoms, the calculation of electron states reduces to the solution of a one-dimensional differential equation whose numerical solutions are no more difficult to obtain than those for a finite square well. A method used by our students is discussed in this paper for the calculation of the electron wavefunctions in a central-field potential. By working this problem, students obtain meaningful results that give them insight into the theory of atomic structure. Results of their experience are included, and possibilities of extending this example are discussed.
We study algorithm to calculate the time dependent Schrödinger equation numerically and to visualize the results. We extend the product formula by the Trotter-Suzuki decomposition to cases of Hamiltonians with vector potentials. This method is unconditionally stable and it can be used for a time dependent Hamiltonian so that one can apply it to various problems without any difficulty. After examining numerical errors for time evolutions of one dimensional wave packets, we present the errors under a constant magnetic field. Also we discuss a cyclotron motion in quantum mechanics, where an advantage for the unconditional stability is demonstrated. In order to visualize the results we make animations of the time evolutions, where the phase of the wave function is represented by colors and its absolute value is shown by brightness. Here we suggest a new way to represent a complex number by colors.