Consider the wave function where n is some positive integer. This function is purely sinusoidal (with wavelength ) on the interval -n < x 2

Consider the wave function

where n is some positive integer. This function is purely sinusoidal (with wavelength λ) on the interval -nλ 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?

(x, 0) = 2/. 0, < x < nk, otherwise,