problem with integration of gaussian distribution


On Mon, 6 Jul 2009, Robert Riemann wrote:

< 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);

Note that x does not appear in the rhs. Also, I think you want to write 

integrate(...)$
psi(x,t) := ''%;

This will compute the integral once.

< 
< 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?

Try:
integrate(...)$
%,exponentialize$
psi(x,t) := ''%;

The second line does what it says.
 
Leo

-- 
The University of Edinburgh is a charitable body, registered in
Scotland, with registration number SC005336.