Quantum Mechanical Potential Well

This applet was created as an extension of the potential barrier applet. For details of how to set up and solve the equations see the supporting documentation for the potential step.

The potential well applet allows the user to visualise the wavefunction of a particle as it passes over a potential well, shown in shaded grey, and to see the wavefunctions inside a well. The wavefunctions are shown underneath the energy level diagram.

• What you see are the real part of the wavefunction (blue), the imaginary part (yellow) and the probability density (violet) for electrons impinging from the left.
• The energy of the electrons is shown by a red line whose height can be adjusted in the range 0 to 10 eV by left clicking on the red line above the well and dragging it up and down. Once activated, you can use the up and down arrow keys to alter the electron energy.
• When the red line is dragged below the zero potential only the discrete bound states can be selected. See references below.
• The well depth is fixed at 10eV.
• The width of the well can be altered by right clicking and dragging the right hand wall of the well to the left or right. Once activated, you can alternatively use the left and right arrow keys to decrease or increase the well width.
• The slider to the right of the wavefunctions can be used to alter the vertical scaling of the wavefunctions. With 200% at the top and 0% of the original wavefunctions height at the bottom.
• The box at the top shows the (fixed) well depth height (labelled Potential), the electron energy (in red), the excess energy the electrons have with respect to the bottom of the well, the well width and the number of electron wavelengths that can fit in the well.
• The scale allows you to estimate the wavelength of the wavefunctions.
• Beneath the wavefunctions are the equations and coefficients used to display the the wavefunctions.

Hidden features

• Left click on the University Logo to decrease the scale to 1Å.

References

• Quantum Mechanics 3rd Ed. AIM Rae. IOP Publishing 1998
• Quantum Physics S Gasiorowicz. John Wiley and Sons 1974

Known Problems
There are a few minor bugs in this program relating to the bound state energy levels. The states can 'pop' out of the well before they should do. This is due to the discrete values that the well width is fixed to.
When the scale is reduced to 1Å only the ground state energy level is displayed. This is correct but when the well becomes less than 0.3Å in size this energy level pops off the top. Providing no attempt is made to click on the level, decreasing the well width further will still produce the desired result.
If the energy level is selected the code will break down and the wavefunctions will be displayed incorrectly. If this does happen, right clicking to change the barrier width will return the display to its correct value.
The applet and web pages were designed by Gary Skinner, as part of a project sponsored by LSTN.