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Radial Solution of Hydrogen Model

Shodor > CSERD > Resources > Models > Radial Solution of Hydrogen Model

  Software  •  Instructions  •  Theory

Instructions - Radial Solution of Hydrogen Model


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.


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

The Graph

The graph shows the value of $y_l(t)$, where $t = 50 - r + 0.0001$. 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 $y_l(r)$ versus $r$.

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 $l$ and $\nu$.

Things to try

Using the bar graph view, set the time to 50 and leave it at that value. ($t=50$ is the end of the calculation, or the value of $y_l(r)$ 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 $y_l(r)$ at the center of the atom. For what values of $l$ and $\nu$ are $y_l(r=0)=0$?

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