(a) Using the integral in Problem 39.68, determine the wave function (x) for a function B(k) given...

(a) Using the integral in Problem 39.68, determine the wave function ψ (x) for a function B(k) given by This represents an equal combination of all wave numbers between 0 and k0. Thus ψ (x) represents a particle with average wave number k0/2, with a total spread or uncertainty in wave number of k0. We will call this spread the width wk of B(k), so wk = k0.
(b) Graph B(k) versus k and ψ (x) versus x for the case k0 = 2π/L, where L is a length. Locate the point where ψ (x) has its maximum value and label this point on your graph. Locate the two points closest to this maximum (one on each side of it) where ψ (x) = 0, and define the distance along the x-axis between these two points as wx the width of ψ (x). Indicate the distance wx on your graph. What is the value of wx if k0 = 2π/L?
(c) Repeat part (b) for the case k0 = π/L.
(d) The momentum p is equal to hk/2π, so the width of B in momentum is wp = hwk/2π. Calculate the product wp wx for each of the cases k0 = 2π/L and k0 = π/L. Discuss your results in light of the Heisenberg uncertainty principle.