The wave function of free particle initially at time t=0 is given by the wave packet
$\psi(x, 0) = [2\pi(\Delta x)_0^2]^{-1/4} exp \{ - \frac{x^2}{4(\Delta x)_0^2} + ik_0x \}$
where $(\Delta x)_0^2$ represents the initial width of the wave packet (i.e. the variance).
a) Determine the wave function for the free particle at some later time t,
$\psi(x, t)$.
b) What is the width (the variance) of the wave packet at the later time t?
