Consider the wave functionwhere n is some positive integer. This function is purely sinuso...

Consider the wave function

where n is some positive integer. This function is purely sinusoidal (with wavelength k) on the interval —nkp, 0). Sketch the graphs of  and, and determine their widths, wx and wp (the distance between zeros on either side of the main peak). Note what happens to each width as n → ∞. Using wx and wp as estimates of ∆x and ∆p, check that the uncertainty principle is satisfied. Warning: If you try calculating σp, you're in for a rude surprise. Can you diagnose the problem?