This java applet is a quantum mechanics simulation that shows the interaction of classical electromagnetic radiation with a particle, in one dimension. This applet will make more sense if you have already used the Quantum States applet.

At the top of the applet you will see a graph of the potential, along with horizontal lines showing the unperturbed energy levels. By default it is an infinite square well (zero everywhere inside, infinite at the edges). The electric field will cause the floor of the well to move slightly; you will be able to see this movement better if you turn up the radiation intensity.

Below the potential graph you will see an arrow showing the direction and magnitude of the electric field, and the current caused by the particle's motion. (The particle is assumed to be positively charged, and the current is assumed to be proportional to d<x>/dt.) Below that you will see the probability distribution of the particle's position. At the bottom of the screen is a set of phasors showing the current particle state.

Underneath the phasors is set of circles showing possible final states; the blue color indicates the transition rate to that state (assuming the correct frequency is chosen). The darker the blue color, the faster the transition; transitions which are extremely slow or forbidden by selection rules are shown as black.

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

When the applet starts up, there is an incoming wave which is at the right frequency (the Bohr frequency) to transition the particle from the ground state to the first excited state. Once it reaches the first excited state, it transitions back to the ground state, and so on.

To view another transition, double-click the appropriate state phasor to put the particle in that state. Then click the final state underneath it. This will start an incoming wave with the right frequency to make that transition. The initial and final states will be shown in purple.

If you transition from a lower state to a higher state, that is called absorption; the particle will absorb energy from the incoming wave. In that case the current will be in phase with the electric field, which would cause the wave to weaken somewhat in real life (but not in this simulation).

If you transition from a higher state to a lower state, that is called stimulated emission; the particle will lose energy. In that case the current will be out of phase with the electric field, which would cause the wave to get stronger (energy will be radiated away).

In order to simulate spontaneous emission, we need to quantize the electromagnetic field. Since the wave in this applet is treated classically, we can't do spontaneous emission.

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

• Infinite Well: this is the "particle in a box"; the particle is confined between two walls of infinite potential.
• Coupled Well Pair: this is two square wells with a wall between them.
• Harmonic Oscillator: this is a harmonic oscillator potential. This potential is unusual because the energy levels are evenly spaced. So when transitioning from the ground state to the first excited state, the particle will keep going into the second excited state and then third excited state, etc., because the Bohr frequency for the first two states is also the Bohr frequency for the next two states. The effect of this is that the particle will stay in a coherent state where it moves from side to side without changing shape, and will will keep acquiring more and more energy, just like a classical particle in a forced harmonic oscillator at resonance. (After a while the particle will go too far to the sides and will become deformed; that is an artifact of this applet and would not happen in a real harmonic oscillator.)

The Clear button clears out all states.

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 Stop Radiation button stops the incoming wave. The wave will start again when you select a final state or adjust the frequency slider.

The Reverse Phase button reverses the phase of the incoming wave, which also reverses the direction of energy flow.

The Stopped checkbox stops the simulation temporarily.

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

The Radiation Intensity slider changes the intensity of the incoming radiation. When the radiation is more intense, transitions will proceed more quickly, but they might be "messier" because of secondary transitions that would otherwise be too weak to have an effect.

The Radiation Frequency slider changes the frequency of the incoming radiation. Normally this is set automatically by choosing the initial and final state, but it can also be set manually. If you modify this at all, then you will not get exact resonance and transitions will be much less likely to happen.

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 View Menu has the following items:

• Position: show the position graph (on by default)
• Momentum: show the momentum graph
• Parity: show a graph of parity.
• Probability Current: show the probability current. This is zero for stationary states. For states that are not stationary, the probability current is positive where the wave function is moving to the right and negative where it is moving to the left.
• Expectation Values: show expectation values as red lines
• Uncertainties: show uncertainties as blue lines to the left and right of the expectation value. The distance from the blue lines to the red line is the uncertainty. This is not available on the probability current graph, because that is not an observable.
• Wave Function: display the wave function in one of four ways: as a probability (magnitude squared), as a probability with the phase shown using colors, as real and imaginary parts graphed separately, or as a magnitude with the phase shown using colors.

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