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A particle is in a one-dimensional harmonic oscillator potential (ħ = 2m = 1; ω = k = 2). The states shown are normalized. Shown are ψ and the results of the integrals that give <x> and <x²> and <p> and <p²>.  Vary n from 1 to 10.

1. What do you notice about how <x> and <x²> and <p> and <p²> change?
2. Calculate ΔxΔp for n = 0. What do you notice considering ħ = 1?
3. What is E_n?  How does this agree with or disagree with the standard case for the harmonic oscillator?
4. How much average kinetic and potential energies are in an arbitrary energy state?