## 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 <

*x*

^{2}>, and <

*p*> and <

*p*

^{2}>. Vary

*n*from 1 to 10.

- When you change
*n*, what do you notice about how <x> and <x^{2}>, and <p> and <p^{2}> change? - Calculate Δ
*x*Δ*p*for*n*= 0. What do you notice considering*ħ*= 1? - Calculate Δ
*x*Δ*p*for*n*= 10. How does your result compare to your*n*= 0 result?

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