An electron can be described by a wave function. The wavelength of the electron's wave function is inversely proportional to the square root of the kinetic energy of the electron; that is, when the electron's wavelength is large, its kinetic energy is small.
The square of the amplitude of the wave in a region is proportional to the probability of finding an electron in that region.
In this tutorial we will use a computer program called Quantum Tunneling. It is quite similar to the Wave Function Sketcher that you used previously. We will start with a simple example.
Set up a potential energy diagram similar to the one for an electron in a TV picture tube as it approaches the TV screen (e.g. Like Figure 2 below).
Click on the tab Barrier Parameters, choose a square barrier, adjust the "barrier height" and the "right level" to the same value. You should reproduce a potential energy diagram similar to Figure 2.
You may need to adjust the electron's energy by clicking on the Particle Parameters tab.
Click the blinking Redraw Graphs button. After calculating for a few seconds, the program will display the wave function in the window just below the potential energy diagram. In this program there is no need to calculate de Broglie wavelengths, decrease lengths or to match boundaries.
You should see a wave function similar to Figure 3 below:
The Quantum Tunneling program calculates and plots the real and imaginary components of the wave function. It also plots the probability density and a graph showing tunneling probability for various electron energies.
Click on the tabs above the graph and have a look at these four representations of the wave function. We will only use the Real and Probability Density tabs in this course.