Physlet Quantum Physics by Belloni, Christian, and Cox: Problem 10.4

10.1: Classical Particles and Wave Packets in an Infinite Well
10.2: The Quantum-mechanical Infinite Square Well
10.3: Exploring Changing Well Width
10.4: Time Evolution
10.5: Classical and Quantum-mechanical Probabilities
10.6: Two-state Superpositions
10.7: Wave Packet Dynamics
10.8: Exploring Wave Packet Revivals with Classical Analogies

Problem 10.4: Determine the time-independent expectation values for a two-state superposition

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A particle is in a superposition state in a one-dimensional box of length L = 1. The states shown are normalized and is an equal mix of the two states n₁and n₂for the infinite square well, Y_n1n2(x) = (1/2)^−1/2[ψ_n1(x) + ψ_n2(x)]. Vary n₁ and n₂. The results of the integrals that give <x> and <x²> and <p> and <p²>. You may vary n from 1 to 10. Restart.

What do you notice about the time-independent values of <x> and <x²> as you vary n₁ and n₂?
What do you notice about the time-independent values of <p> and <p²> as you vary n₁ and n₂?

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