PHY 6645 Fall 2002 – Homework 5 Due by 5 p.m. on Monday, October 7. Partial credit will be available for solutions submitted by 5 p.m. on Wednesday, October 9. To gain maximum credit you should explain your reasoning and show all working. Please write neatly and include your name on the front page of your answers. A free particle confined to move in one dimension is described at time t = 0 by the normalized wave function h i ψ(x, 0) = A x exp −(x/2w)2 , (1) where A and w are positive, real quantities. (a) Find A in terms of w and constants. (b) Calculate the position uncertainty ∆X in the state ψ(x, 0). (c) Obtain an expression for the wave function at a time t > 0. Cast your result in a form that is as similar as possible to Eq. (1). (d) Calculate the position uncertainty ∆X in the state ψ(x, t).