**Hydrogen Atom Probability
Density Applet**

When Quantum Mechanics was first discovered, its initial and most important application was to describe the Hydrogen and Hydrogen-like atoms. The hydrogen atom represents one of the few directly solvable problems in Quantum Mechanics because of the 1/r Coulomb potential between the valence electron and nucleus. The Applet above solves the Quantum Mechanical Hydrogenic Wave Function and then paints a picture showing the amplitude of Psi in the x-z plane a certain number of Bohr radii from the nucleus. The reason the Applet graphs the amplitude of Psi instead of the modulus squared (the actual probability of finding the electron an x number of Bohr radii from the nucleus) is due to limitations in the color scale. The probability values are significantly smaller than those of amplitude, so when the values are scaled to a number between 0-255 to correspond to an integer value on the red, green, and blue color scale, it doesn't work. The probability values are too small and too close together so there isn't much variation in the colors assigned to those points, at least not enough for the naked eye to discern since it operates on a logarithmic scale.

To use the Hydrogen Probability Density Applet, simply chose the n,l, and m values that you want and then press the plot button. When choosing, however, you must remember that l can never be larger than n-1 and m can never be bigger than ħm. If you do make a mistake in entering a value, the box into which the incorrect number has been entered will turn red. This applet also can show the phase of hydrogeni wave function. To view the phase, click the radio button with Y next to it for yes, or N for no phase (**a small note: to view the probability density it is best to view without phase as the black and white colors give a better overal idea of probability amplitude**). Please play around with this applet a bit, and then send me your comments (check out the very bottom of the page!).

The Hydrogenic Wave Function consists of a Radial and Angular part. To see these two parts separately please visit my Radial Probability Applet or my colleague Jim Nolen's Angular Probability Applet.

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If you have any comments or questions about this applet, please send them to me at cafisher@davidson.edu.