This exercise uses the "shooting method" to find solutions to the Schrodinger equation for a finite square well potential. Edit the value of the Energy either by typing or by clicking on the 4 buttons to the right of the energy. By trial and error you can find energies that result in the wave function going to zero at the right hand end of the graph. Those correspond to the energy eigenvalues and the eigenfunction solutions to the Schrodinger equation.
You can also type in the desired quantum number in the box to the right of "n=" and click "Find", in which case the program will find the corresponding solution. Note that for sufficiently large energies the solutions will not be bound but will correspond to a particle propagating through the well and on to infinity. If you desire, you may modify the height and width of the potential in the box below the graph. Shallower wells will have fewer bound-state solutions. You may also make more complex changes, such as introducing bump in the middle of the well (Try "-step(x+0.5)*step(0.5-x)*1000 + 1000 + step(x+0.1)*step(0.1-x)*200", for example).
You can also change the energy by right clicking and dragging the energy bar in the energy spectrum plot to the right of the wavefunction. The corresponding wave function solution will update in real time.
Note that the wave function is plotted with the zero of the vertical axis centered on the corresponding energy in the energy spectrum plot. Therefore, the user must understand that the wave function goes to zero when it lines up with the energy bar in the spectral graph to the right.
This Physlet is taken from an example provided in the book "Physlets: Teaching Physics with Interactive Curricular Material," by Wolfgang Christian and Mario Belloni.