Problem 6.4: Calculate position and momentum uncertainties for a particle in a harmonic oscillator

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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. When you change n, 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. Calculate ΔxΔp for n = 10. How does your result compare to your n = 0 result?

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