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This java 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 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. (This is just the fourier transform of the particle's position.) 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. To delete a state, click on the phasor and then drag the mouse far away from it.

Between each graph is a horizontal line which may be dragged up and down to adjust the size of each graph.

Each graph also has a red line, indicating the expectation value for that observable.

The Setup Popup allows you to select a predefined potential. The choices are:

The Mouse Popup determines what happens when the mouse is clicked. The choices are:

The Clear button clears out all states.

The Normalize button normalizes the set of particle states. (By default, the states are not shown normalized because the interface is easier to use if they are not. They are normalized internally when calculating the wave functions, however.)

The Maximize button changes the magnitude of the particle states so that they are all as large as possible. This makes them easier to see. (It won't change the wave function at all because the states are normalized internally.)

The Ground State button selects the ground state wave function.

The Rescale Graphs button changes the scale of all the graphs so that everything is as large as possible. Normally, the scale is adjusted only when necessary, so click this button if the wave functions are too small to see clearly.

The Stopped checkbox stops the evolution of the wave function.

The Simulation Speed slider changes the speed of the wave function evolution.

The Resolution slider changes the resolution of the applet. The higher the resolution, the more accurate the wave functions and energy levels will be.

The Particle Mass slider changes the mass of the particle.

The View Menu has the following items:

The Measure Menu has the following items:

The Options Menu has the following items:

If you like this applet you may be interested in the book Visual Quantum Mechanics.

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