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Problem 10.5: Determine the time evolution of Δx and Δp for a two-state superposition.
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The superposition shown is an equal mix of the two states n1 and n2 for the infinite square well, Yn1n2(x,t) = (1/2)−1/2 [ψn1(x,t) + ψn2(x,t)]. The wave function evolves with time according to the Schrödinger equation. You may change state by choosing an n1 and n2. Time is shown in units of the revival time for the ground-state time-dependent energy eigenfunction of a particle in an infinite square well. In other words, it is the time for the ground-state time-dependent energy eigenfunction to undergo a phase change of 2π. Restart.
- For n1 = 1 n2 = 2, what are Δx and Δp at t = 0?
- For n1 = 1 n2 = 2, what are Δx and Δp at t = 0.093 (1/12)?
- For n1 = 1 n2 = 2, what are Δx and Δp at t = 0.166 (1/6)?
- For n1 = 1 n2 = 2, what are Δx and Δp at t = 0.250 (1/4)?
- For n1 = 1 n2 = 2, what are Δx and Δp at t = 0.333 (1/3)?
- What do you recognize from this pattern and by looking at the wave function?
Vary n1 and n2, from 1 to 10 and consider (a)-(f) for some other combination of n1 and n2.