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Problem 12.2: A particle is in a 1-d dimensionless harmonic oscillator potential
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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.
- What do you notice about how <x> and <x2> and <p> and <p2> change?
- Calculate ΔxΔp for n = 0. What do you notice considering ħ = 1?
- What is En? How does this agree with or disagree with the standard case for the harmonic oscillator?
- How much average kinetic and potential energies are in an arbitrary energy state?