Quantum Mechanics may not be everybody’s cup of tea, but today’s servings are laced with sweeteners that make a cup worth sipping.
It might be straightforward to show the basic principle of a particular time-independent problem using either a single or a short series of figures for the wave function and the probability distribution. However, it wouldn’t be as easy if we wanted to talk about time-independent ones. This is clearly a job for simulations. Programs that show simulations of time-dependent wave functions can be more sophisticated to write but there are already existing applications that we can use. The best thing is that, they’re free. While there are definitely other sites that allow you to download similar applications, I recommend you start with http://www.compadre.org/osp/. It houses packages that combine computer simulations with tutorial materials and student worksheets. The simulations included in these packages are written in Java. Hence, one has to have the Java Virtual Machine (JVM) for the applications to run in his/her operating system.
Simulations temporarily take the math (and the burden of plotting) out of the equation and let you focus on the physics part of a particular problem. Consider the simple particle in a box problem. By changing values of n in the program, one can automatically see how the wave function and the probability distribution varies. Below are screenshots of the Free Particle Wave Packet Program, which shows how a wave packet evolves with time in the position and momentum space. Without having to go through a rigorous mathematical discussion, the user easily sees how the wave packet spreads in position space but remains constant in momentum space. Using simulations as a pedagogical tool allows the learner to experience the event and empowers him to make observations of his own. These observations can later be verified in his readings or mathematical derivations. Regardless of whether he interprets all his observations correctly, the point of the whole exercise is that the interest of the learner is captured and he is given the chance to “see” the event as it happens.