Eigenvalue Applet Beta Version 0.9: Harmonic Oscillator Example

This applet simulates the parabolic potential of a harmonic oscillator problem and allows one to find the energy eigenvalues of the wave function Psi.  To view the wave functions that correspond to the green energy levels on the right of the graph, left click the mouse and drag over them.   You can find other energy levels by using the "find button".  Just enter the energy eigenvalue that you are searching for into the box to the right of the button and it will find it for you.  Otherwise, to go through the entire energy spectrum, right click and drag the mouse in the energy level diagram to the left. This will calculate the wave function at that particular spot on the energy spectrum.  The buttons labelled <<,<,>,>> allow you to navigate around the energy levels in small steps to better see them converge.

If you are a professor and are interested in using this applet in your curriculum, there are several variables that one can script in that allow you to better tailor the problem to your needs. The HTML "parameters" available for scripting in this applet are seen directly below:

PARAM NAME = "XMin" VALUE = "-5" -->sets the min value on x-axis

PARAM NAME = "XMax" VALUE = "5" -->sets the max value on x-axis

PARAM NAME = "YMin" VALUE = "0" -->sets the min value on y-axis

PARAM NAME = "YMax" VALUE = "32" -->sets the max value on y-axis

PARAM NAME = "Potential" VALUE = "x*x"-->sets the potential to be studied

PARAM NAME = "ShowControls" VALUE = "true"-->hides/shows the control panel

PARAM NAME = "HBarTwoM" VALUE = "1"-->sets the quantum constant h/2m

PARAM NAME = "Lowest" VALUE = "1"-->The lowest energy eigenvalue to calculate intially

PARAM NAME = "Highest" VALUE = "6"-->The highest energy eigenvalue to calculate intially

PARAM NAME = "NumPts" VALUE = "302"-->the number of data points to be graphed

PARAM NAME = "ShowSpectrum" VALUE = "true"-->boolean to show the energy level diagram or not

PARAM NAME = "ShowPotential" VALUE = "false"-->hides/shows the potential input text box

PARAM NAME = "Tolerance" VALUE = "1e-8" -->the accuracy value for the wave function

These are the actual parameters used in this specific Harmonic Oscillator problem. They should be fairly self-explanatory and allow a great deal of freedom to the instructor in terms of setting up a specific energy-eigenvalue problems. Just simply embed this text inside the APPLET and /APPLET tags on your HTML page with the paramaters that suit you. I have scripted several other potential examples which can be viewed by clicking on their respective links below.

The Kronig-Penney Model

The Potential Well Example