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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 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?
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