This exercise again uses the QM1D Javascript Applet (below, or here: http://www.

Question

This exercise again uses the QM1D Javascript Applet (below, or here: http://www.falstad.com/qm1d-phys214/qm1d/). Java is required.

Coupled Well Pair

Open the program, which will by default give you the simulation of an "Infinite Well" potential. Instead select the "Coupled Well Pair" potential. Drag the lower right corner to make the window as large as possible.

The top portion of the display will now show the potential plus energy levels; the middle portion shows both the probability density (once you've selected a solution -- just click on one of the energy levels -- or made a superposition), i.e., the absolute square of the wave function, as a filled solid white area, as well as the eigenstate (as a yellow curve) corresponding to the energy level your cursor is nearest to; and the bottom portion with the circles shows the phasors corresponding to each of the eigenstate solutions for the problem.

Sliders on the right side of the display allow you to adjust various parameters. Do this now, setting the Well Separation to 308.46 pm (slider about one fourth from the left), and Wall Potential to -20 eV (slider about one fourth from the left).

Force the system to be in its lowest energy state by clicking on "Ground State". Note that the probability density is constant in time; however, you can see the rotation of the associated phasor—remember, the rotation rate of the phasor is proportional to the energy of the state. (If you don't see the rotation, make sure the "Stopped" box is unchecked.)

Now use the cursor to make an equal superposition of the ground and first excited state: Do this by clicking the mouse inside the second phasor disk (at a point near the rim). You may need to reduce the Simulation Speed (slider to the left). Observe what happens.

Q1. Describe the effect of decreasing the "Wall Potential" (moving the slider slightly to the left).

1. The frequency of oscillation increases.

2. The frequency of oscillation decreases.

3. The frequency of oscillation is unaffected

Q2. Now look at the energy splitting between the ground state and first excited state energy levels (the two horizontal lines just above and below the red horizontal line, which shows the AVERAGE energy). What is the effect of increasing the "Wall Potential"?

1. The energy splitting increases.

2. The energy splitting decreases.

3. The energy splitting is unaffected.

Q3. Describe the effect of increasing the "Well Separation"?

1. The energy splitting increases.

2. The energy splitting decreases.

3. The energy splitting is unaffected.

Explanation / Answer

1. Due to decrease in Wall potential, the frequency of oscillation increases.

2. The energy splitting decreases.

3. The energy splitting decreases.

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