Time dependent Gross-Pitaevsky equation


Giannis
02-21-2006, 03:01 PM
I have been using Mathematica to solve the Gross-Pitaevsky time independent equation in this form:
y''[r] - r^2*y[r]/4 - (p4)^2* y[r]^3 + r* e* y[r] == 0
where y[r] is the wave function, r is the variable of space, p4 is chosen so that y[0]=1 and e is the energy. For different values of e, I have found different wave functions, after finding p4

My question is if somebody could point me in the right direction so as to solve the time dependent equation numerically:

i*dy/dt=-y''[r]+r^2*y[r]/4-w[t]^2*(p4)^2*|y[r]|^2*y[r]

Where w[t] is a function of time which will be chosen for specific solutions. e.g. w[t]=sint-1

I've read a few things about this and I know I should be using
a semi-implicit Crank-Nicholson algorithm. However, I have no idea what this is.

Giannis
05-14-2008, 11:34 PM
It's a model for a Bose-Einstein Condensate at near T=0K, in a time dependent, isotropic, harmonic trap.