Quantum Mechanical Potential Barrier

This applet was created to allow visualisation of the wavefunction of an electron as it passes over a potential barrier, shown in shaded grey. The wavefunctions are underneath the energy level diagram. The applet is a development of an accompanying applet on a quantum mechanical step. See this page for supporting documentation on how to set up and solve the relevant equations.

• 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 20 eV by clicking on the red line to the left of the barrier and dragging it up and down. Once activated, you can use the up and down arrow keys to raise or lower the electron energy.
• The barrier height is fixed at 10eV.
• The width of the barrier can be altered by dragging the right-hand wall of the well to the left or right, up to a maximum of 20 Å. Notice the resonances of the wavefunction within the barrier when the width is right. Once activated you can use the up and down arrow keys to decrease or increase the barrier 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 boxes at the top show the barrier height (labelled Potential), the electron energy (in red), the excess energy the electrons have over the barrier, the barrier width and the number of electron wavelengths that can fit into the barrier.
• The scale allows you to estimate the wavelength of wavefunction.
• Beneath the graphs are the equations and coefficients for the displayed wavefunctions.

Hidden features

• Left click on the University Logo to decrease the barrier width by a factor of 10. The scale changes to show 1 Å.

 The applet and web pages were designed by Gary Skinner, as part of a project sponsored by LSTN.