Physlet Quantum Physics by Belloni, Christian, and Cox: Problem 6.4

6.1: Probability Distributions and Statistics
6.2: Classical Probability Distributions for Moving Particles
6.3: Exploring Classical Probability Distributions
6.4: Probability and Wave Functions
6.5: Exploring Wave Functions and Probability
6.6: Exploring Wave Functions and Expectation Values

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.

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

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