Use your Uncle Paul\'s applet to study the behavior of superposition states in t

Question

Use your Uncle Paul's applet to study the behavior of superposition states in the simple harmonic oscillator potential. http: //www.lalstad.com/qm1d/ Compare the time-dependent probability distributions, the time-dependent expectation values (shown by the red lines), and the time-dependent uncertainties (shown by the blue lines) for the following 50: 50 superpositions for the simple harmonic oscillator: 0 and 1, 0 and 2, 0 and 3, 1 and 2, 1 and 3, 1 and 4. (These states are 1, 2, and 3 steps apart.) Are the time-dependent x-space probability distributions even, odd, or mixed? Are the time-dependent p-space probability distributions even, odd, or mixed? Which quantities are time-dependent and which quantifies are time-independent? For the quantifies that are time-dependent, what is the oscillation frequency? For the quantifies that are time-dependent, what is the relative phase between x-space and p-space?

Explanation / Answer

1. The time dependent x-space probability distributions will always be odd, as can be seen with the help of simulation.

2. Time dependent p-space prob distribution is always even.

3. Probabilty is time independent, while energy and potential are time dependant.

4.Frequency would be 0.5 Hz.

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