This java applet is a quantum mechanics simulation that shows the behavior of a particle in a two dimensional harmonic oscillator.
At the top of the screen, you will see a cross section of the potential, with the energy levels indicated as gray lines. The red line is the expectation value for energy.
In the center of the applet, you will see the probability distribution of the particle's position. The color indicates the phase. At the bottom of the screen is a set of phasors showing the magnitude and phase of some of the possible states.
You may 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. When you move the mouse over a state, it is highlighted in yellow, and other states with the same energy are also highlighted.
You may create a gaussian wave packet by clicking and dragging on the position graph.
Between each graph is a horizontal line which may be dragged up and down to adjust the size of each graph.
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 Stopped checkbox stops the evolution of the wave function.
The Alternate Rendering checkbox is used to speed up rendering, but it actually slows things down on some machines. (Internally, it uses the MemoryImageSource class instead of drawing a bunch of rectangles.) It should be set to the proper setting by default, but try selecting or unselecting it to see if it speeds things up.
The Simulation Speed slider changes the speed of the wave function evolution.
The Brightness slider controls the brightness, just like on a TV set.
The Resolution slider changes the resolution of the applet. There are only two possible resolutions.
The Aspect Ratio slider will adjust the strength of the "spring constant" in the x direction as compared to the y direction.
The View Menu has the following items:
The Measure Menu has the following items:
The Options Menu has the following items:
If neither one of these items is selected, then the applet will maximize the state coefficients whenever major changes are made, and leave them alone otherwise.
On the right side of the phasor panel, you will see a phasor all by itself. This phasor's rotation has the same period as the oscillation of the wave function. Create a gaussian to see this. It is only present if the aspect ratio is square.
If you like this applet you may be interested in the book Visual Quantum Mechanics.