problem with integration of gaussian distribution

Hi all,

i have problems to get Maxima solve an integral about a
bell-shaped curve with a weighting function phi.

I tried it with the following code:

assume( m > 0, d > 0, h > 0, A > 0)$
phi(p) := A*exp(-(p-p_0)^2/(h/d)^2);
psi(x,t) := integrate(phi(p)*(2*%pi*h)^(-1)*exp(%i/h*(p*x-p^2/(2*m)*t)),p,minf,inf);

The result should be a bell-shaped curve to.

What do i have to do to get a human-friendly solution (not with sin, cos, but exp) of this integral?
Is this possible with maxma/wxmaxima?

btw: psi is a state function, that can be found in quantum-mechanics,physics


Hope someone can help me...

Greets Robert