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The two-state superpositions shown are an equal mix of the two states n₁ and n₂ for the harmonic oscillator. The wave function evolves with time according to the Schrödinger equation. You may change states by choosing different values for n₁ and n₂. 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.

1. For each state shown, what is the frequency of oscillation?
2. Are there any states shown where <x> = 0?
3. Are there any states shown where <p> = 0?