Instructions - Radial Solution of Hydrogen Model

Purpose

The purpose of this model is to solve the radial portion of Schrodinger's wave equation for a central potential given by the Coulomb attraction between the proton and the electron in a Hydrogen atom.

The radial hydrogen model was solved using Stella, and turned into an applet using the Stella2Java program.

Stella does not allow for a dependent variable other than time, and also does not allow for integration in a negative direction, however, the standard solution to the radial for of Schrodinger's equation with a central potential is to integrate with respect to radius, and to do so from a distance far from the atom to near the center of the atom.

This can be circumvented using a substitution of variables (in this case r = 50 - t + 0.0001, integrated from t = 0 to 50 to bring r from far away to very close to the center) but a graph of y will appear "backwards" to some students.

Fundamentals

The applet has 2 main sections: the graph and the parameter controls.

The Graph

The graph shows the value of , where . This currently makes the graph appear "backwards". At some point a scatter plot option will be added to the applet to directly allow plotting of versus .

You may view the graph either as a line graph, automatically scaled to fit in the window to a maximum value of 1, or you may view an animation of the value from far away to the center of the atom as a bar graph.

Parameter Controls

You can use the sliderbars or directly enter values of and .

Things to try

Using the bar graph view, set the time to 50 and leave it at that value. ( is the end of the calculation, or the value of close to the center of the atom.) Change the parameter values. Notice that you can immediately see the effect of changing parameter values on the value of at the center of the atom. For what values of and are ?