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 the boundary conditions (a) = (b) = 0; 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.

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.

This screen from the first example notebook shows &;the n=4 and n=10 wave functions calculated by Schrödinger.m.