Consider the wave function

where n is some positive integer. This function is purely sinusoidal (with wavelength λ) on the interval -nλ < x 2 and |Φ (p,0)|², and determine their widths ω_x, and ω_p (the distance between zeros on either side of the main peak). Note what happens to each width as n → ∞. Using ω_x, and ω_p as estimates of Δx and Δp, check that the uncertainty principle is satisfied. Warning: If you try calculating σ_p, you’re in for a rude surprise. Can you diagnose the problem?

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Ψ(x, 0) = —ρί2ππ/λ. η απλ 0, –ηλ < x < nk, otherwise,