Problem 10.5

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The superposition shown is an equal mix of the two states n₁ and n₂ 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 n₁ and n₂.  Time is shown in units of the revival time for the ground state wave function of a particle in an infinite square well.  In other words, it is the time for the ground state wave function to undergo a phase change of 2π.    Restart. 

1. For n₁ = 1 n₂ = 2, what are Δx and Δp at t = 0?
2. For n₁ = 1 n₂ = 2, what are Δx and Δp at t = 0.093 (1/12)?
3. For n₁ = 1 n₂ = 2, what are Δx and Δp at t = 0.166 (1/6)?
4. For n₁ = 1 n₂ = 2, what are Δx and Δp at t = 0.250 (1/4)?
5. For n₁ = 1 n₂ = 2, what are Δx and Δp at t = 0.333 (1/3)?
6. 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. 

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