## Problem 10.5: Δ*x* and Δ*p* time evolution for a two-state superposition

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The superposition shown is an equal mix of the two states *n*_{1 }and *n*_{2 }for the infinite square well, Y_{n1n2}(*x*,*t*) = (1/2)^{−1/2 }[ψ_{n1}(*x*,*t*) + ψ_{n2}(*x*,*t*)]. The wave function evolves with time according to the Schrödinger equation. You may change state by choosing an *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 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
*n*_{1}= 1*n*_{2}= 2, what are Δ*x*and Δ*p*at*t*= 0? - For
*n*_{1}= 1*n*_{2}= 2, what are Δ*x*and Δ*p*at*t*= 0.093 (1/12)? - For
*n*_{1}= 1*n*_{2}= 2, what are Δ*x*and Δ*p*at*t*= 0.166 (1/6)? - For
*n*_{1}= 1*n*_{2}= 2, what are Δ*x*and Δ*p*at*t*= 0.250 (1/4)? - For
*n*_{1}= 1*n*_{2}= 2, what are Δ*x*and Δ*p*at*t*= 0.333 (1/3)? - What do you recognize from this pattern and by looking at the wave function?

Vary *n*_{1} and *n*_{2}, from 1 to 10 and consider (a)-(f) for some other combination of *n*_{1} and *n*_{2}.