This applet is a quantum mechanics simulation that shows the behavior of a single particle in bound states in one dimension. It solves the Schrödinger equation and allows you to visualize the solutions.
At the top of the applet you will see a graph of the potential, along with horizontal lines showing the energy levels. By default it is an infinite square well (zero everywhere inside, infinite at the edges). Below that you will see the probability distribution of the particle's position, oscillating back and forth in a combination of two states. Below the particle's position you will see a graph of its momentum. At the bottom of the screen is a set of phasors showing the magnitude and phase of all the possible states.
To view a state, move the mouse over its energy level on the potential graph. To select a single state, click on it.
You may also select a single state by picking one of the phasors at the bottom and double-clicking on it. Or, you may click on the phasor and drag its value to modify the magnitude and phase. In this way, you can create a combination of states.
You may select a different potential from the Setup menu at the top right.
This wonderful applet and many others like it can be found at Paul Falstad's Math and Physics page: www.falstad.com/mathphysics.html We'll be referring to a number of these applets during the semester.