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).