This Physlet shows the solution to Schroedinger's equation for a particle inside an infinite square well. It is solved using the "shooting method" in which an initial guess for the energy is made. After each iteration the result is compared to the known boundary value and the energy is refined until an acceptable tolerance level is reached. In this problem the trial solution to the wavefunction is calculated from left to right.
In this case the boundary condition is that the wave function must go to zero at the sides of the well. Note that the wave function is plotted such that zero on the vertical scale lines up with the energy level in the spectral plot on the right. The wave function always starts from zero at the left wall. Adjust the energy up or down until it also matches zero at the right wall. You can also find the solutions by entering the desired quantum number in the box on the lower right and clicking "Find". Note that the corresponding energy, however, is displayed in that case to only 3 decimal places.
This Physlet is taken from an example provided in the book "Physlets: Teaching Physics with Interactive Curricular Material," by Wolfgang Christian and Mario Belloni.