Radial Probability Applet

           This applet plots the Radial probability of the Hydrogenic wave equation.  It does so by solving the radial portion of the hydrogenic Schrodinger wave equation, Rnl(r), and then calculating the probability by the relation P(r)= [Rnl(r)]2 *r2.   It can also show the amplitude of just the wave function by clicking here (Click here to see probability amplitude again).  The algorithm is carried out and the results graphed when the user presses the "Plot" button.  To view a superpostion of states, or several states at once, click the "Show Multiple" checkbox.  Otherwise, enter your chosen n and l values into their respective boxes.  I hope you enjoy this applet! 

   **Interestingly enough, when searching for the proper form of the hydrogenic radial wave equation to use, I encountered a major problem.  In all of the texts that I referenced, the normalization constants did not give the correct probability values (ie the normalized wave function probability values did not all sum up to the expected value of 1!).   Therefore, being the die hard physicist that I am, I began my quest to find the correct normalization constant for the radial wave equation given in all of the text books.  After a lot of help and prodding from Dr. Belloni (a quantum physicist) and Dr. Christian, we were finally able to derive the correct constant that normalized the text's radial wave function (ie all probability values finally summed up to 1!).  Click here to see the derivation.

My colleague, Jim Nolen, wrote an applet that solves the Angular portion of the Hydrogen wave equation.  See it here.

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