Numerical Domain
xmin = -3
xmax = 3
Nx = 3000
CFL = 0.125
Nt = 960000
Initial Conditions (ground state of the potential)
omega = 12.5d0*pi
psi = (omega/pi)**0.25 *exp(-0.5*omega*x**2)
Potential
V(t) = 0.5d0 * (omega*x)**2 + 0.2*omega**2*sin(omega*t)*x
