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# Problem 12.3: Two-state superpositions in the harmonic oscillator

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The two-state superpositions shown are an equal mix of the two states *n*_{1} and *n*_{2} for the harmonic oscillator. The wave function evolves with time according to the Schrödinger equation. You may change states by choosing different values for *n*_{1} and *n*_{2}. Time is shown in units of the revival time for the ground-state time-dependent energy eigenfunction of a particle in a harmonic oscillator. In other words, it is the time for the ground-state time-dependent energy eigenfunction to undergo a phase change of 2π.

- For each state shown, what is the frequency of oscillation?
- Are there any states shown where <
*x*> = 0? - Are there any states shown where <
*p*> = 0?

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