 |
|
|
|
|
||
|
Schroedinger.m: A Mathematic Package for Solving the
Time-Independent Schrödingier Equation
|
||
|
John C. Hanse
Southwest State University, Marshall, MN 56258 |
||
|
|
||
|
Note: |
This program is included in the Advanced Chemistry Collection (SP-28).
To Order Advanced Chemistry Collection |
|
|
|
||
|
Schroedinger.m enables the user of Mathematica (1), to define a potential and determine bound-state energy eigenvalues for a one-dimensional Hamiltonian. A Windows version of this program (2) has recently been published. Schroedinger.m defines commands in Mathematica to set the potential, solve the Schrödinger equation to obtain both energies and wave functions, display the solutions graphically, and calculate certain integrals involving the wave functions. It is limited to one-dimensional bound-state problems with fixed boundary conditions; it cannot be applied to other one-dimensional problems with periodic boundary conditions. It is well suited to solving the one-dimensional R-dependent Schrödinger equation that describes most diatomic molecular potentials. Students new to both quantum mechanics and Mathematica find Schroedinger.m easy to use. It can be used in a junior-level physical chemistry course to provide examples or to provide the means for students in such a course to carry out numerical experiments. The commands defined in the package require only elementary knowledge of Mathematica. However, the more Mathematica one knows, the further one can go with the applications. Knowing even a very few basic Mathematica functions enables a student to use solutions from this package to do some fairly sophisticated computations with one-dimensional wave functions. A student does not need to know the details of Schroedinger.m in order to use it. However, it helps to be able to understand how the computer represents the solutions in order to move beyond the simplest applications or to understand the limitations of the package. The numerical method used is described in detail in the program documentation. The user has direct control over parameters that define the extent of the grid, its spacing, and the range of solutions. In many cases, however, it is not necessary to worry about these numerical parameters. Simply using built-in defaults gives an adequate answer. However, to apply the method to an unusual or complex problem, it may be necessary to carefully consider how to set these parameters. Fortunately, the methods for doing so are fairly straightforward. Hardware and Software Requirements Software in Series C of JCE: Software requires an Apple Macintosh computer with 4 MB RAM, a hard drive, and a SuperDrive floppy disk drive. System software version 7 or later is required. In addition, Schroedinger.m requires a version of the Mathematica program with notebook-type interface; at least 8 MB of RAM. Literature Cited |
||
|
|
|
|
|
|
|
|
|
|
|
|
|
Last Updated: July 19, 2001 Created: |
Created by: S. B. Mathews Comments to: jceonline@chem.wisc.edu |
|
|
|
| © 1997 Division of Chemical Education, Inc., American Chemical Society. All rights reserved. | |