Electrons in Hydrogen

The following applet will show you a full three dimensional plot of the wave function for one or two electrons in a Hydrogen atom (for a single electron, set "n2" to zero). Push the "replot" button to redraw the plot. The scroll bars allow you to change n, l and m for each electron. Electron 1's wave function is plotted in magenta, and electron 2's wave function is plotted in cyan. The two colors add to blue or white where the wave functions overlap. To change the perspective, drag the mouse across the window; to zoom, turn the scroll wheel.

This applet comes with a caveat: when plotting the wave function for two electrons, the mutual interaction of the electrons has been ignored. This is an unfortunate necessity caused by the complexity of the equations of quantum mechanics: the applet only knows solutions in closed form for individual electrons in a single-electron atom. But the plots still exhibit the essential qualities of the electron wave functions that interest us.

Please be patient: each plot requires the evaluation of each wave function at over 3.5 million points! The "Replot" button will be labeled with ellipsis while the evaluation process is taking place.

You need a Java-capable browser to be able to use the applets. If they do not work with your Windows system, download the Java VM (Virtual Machine) for your version of Windows at the download section at java.sun.com.

©2014, Kenneth R. Koehler. All Rights Reserved. This document may be freely reproduced provided that this copyright notice is included.

Please send comments or suggestions to the author.