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Schrödinger Equation Eigensystem Model
written by Wolfgang Christian
The Schrödinger Numerov Eigensystem Model solves the time-independent Schrödinger Equation with arbitrary potential energy V(x) using the Numerov method recast on a discrete lattice. As shown by Pillai, Goglio, and Walker, the resulting matrix eigenvalue problem can be solved with just a few lines of code.  In this model, we demonstrate how to do this computation in Java using the linear algebra package in the Apache Commons Math library.  Users can adjust the location of the hard hard walls at x-minimum and x-maximum and the potential V(x) in the region between the walls.  The main window shows the potential and the energy eigenvalue spectrum along with a superimposed wave function psi.  A second window shows the normalized wave function. The energy eigenvalue can be set by dragging the cursor in the main window or by entering the quantum number n.

The Schrödinger Numerov Eigensystem Model was developed using the Easy Java Simulations (Ejs) modeling tool.  It is distributed as a ready-to-run (compiled) Java archive.   Double clicking the jar file will run the program if Java is installed.  You can modify this simulation if you have EJS installed by right-clicking within the map and selecting "Open Ejs Model" from the pop-up menu item.

Please note that this resource requires at least version 1.6 of Java.
1 source code document is available
Subjects Levels Resource Types
General Physics
- Computational Physics
Mathematical Tools
- Linear Algebra and Tensors
Quantum Physics
- Approximation Techniques
- Bound State Systems
- General
- Upper Undergraduate
- Graduate/Professional
- Lower Undergraduate
- Instructional Material
= Interactive Simulation
Intended Users Formats Ratings
- Learners
- Professional/Practitioners
- Educators
- application/exe
- application/java
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Access Rights:
Free access
This material is released under a GNU General Public License Version 3 license.
Rights Holder:
Wolfgang Christian
energy eigenfunctions, energy eigenstates, quantum mechanics
Record Cloner:
Metadata instance created November 14, 2012 by Wolfgang Christian
Record Updated:
June 12, 2014 by Andreu Glasmann
Last Update
when Cataloged:
November 14, 2012
Other Collections:

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Record Link
AIP Format
W. Christian, Computer Program SCHRÖDINGER EQUATION EIGENSYSTEM MODEL, Version 1.0 (2012), WWW Document, (
W. Christian, Computer Program SCHRÖDINGER EQUATION EIGENSYSTEM MODEL, Version 1.0 (2012), <>.
APA Format
Christian, W. (2012). Schrödinger Equation Eigensystem Model (Version 1.0) [Computer software]. Retrieved January 16, 2017, from
Chicago Format
Christian, Wolfgang. "Schrödinger Equation Eigensystem Model." Version 1.0. (accessed 16 January 2017).
MLA Format
Christian, Wolfgang. Schrödinger Equation Eigensystem Model. Vers. 1.0. Computer software. 2012. Java 1.6. 16 Jan. 2017 <>.
BibTeX Export Format
@misc{ Author = "Wolfgang Christian", Title = {Schrödinger Equation Eigensystem Model}, Month = {November}, Year = {2012} }
Refer Export Format

%A Wolfgang Christian
%T Schrödinger Equation Eigensystem Model
%D November 14, 2012
%O 1.0
%O application/java

EndNote Export Format

%0 Computer Program
%A Christian, Wolfgang
%D November 14, 2012
%T Schrödinger Equation Eigensystem Model
%7 1.0
%8 November 14, 2012

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Schrödinger Equation Eigensystem Model:

Is Based On Easy Java Simulations Modeling and Authoring Tool

The Easy Java Simulations Modeling and Authoring Tool is needed to explore the computational model used in the Schrödinger Equation Eigensystem Model.

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