Computer assisted learning

Abstract

SCHROE, a graphic interactive program, studies the one-dimensional time-independent Schroedinger's equation for three symmetrical potentials: infinite depth square well, harmonic oscillator, anharmonic oscillator.The student enters an energy value and obtains the plot of the unnormalized solution of the equation, computed by the "middle point" numerical integration method. By visual analysis of the plot of the solution displayed on the terminal screen, the student determines whether the input energy value is or is not an eigenvalue. He or she can build a succession of solutions converging towards the eigenfunction, exploiting the property that the solution diverges to plus or minus infinity for energy values greater than or less than the eigenvalue.The choice of integrating the equation by a numerical method allows one to obtain a solution when no analytical solution exists, and to compare the result with the analytical solution when it is available.When the energy is an eigenvalue, the program displays in addition the plot of the probability density of finding the particle.The program is being tested on groups of volunteer students.