Energy Eingenvalues with slider.

Bound Particle Energy Eigenstates and the Shooting Method

Description

A particle is confined to a box with hard walls at x = -3 and x = 3 and an unknown potential energy function within the box.  Change the energy slider and examine the solutions to the Schroedinger equation for this system.

Questions

  1. Estimate the energy of the ground state my moving the slider.  Enter the energy value 4.86346 in the slider text box.

  2. How many eigenstates are there between E=0 and E=20?

  3. Estimate  the energy eigenvalues for the system between E=0 and E=20? Use a procedure similar to the following:

  4. Test the next digit in the the same manner until you reach the desired precision.

  5. Examine each eigenfunction and sketch a reasonable potential energy function that is consistent with your observations.

Credits

Script by Wolfgang Christian.
Questions by Wolfgang Christian.
Java applets by Wolfgang Christian.