I need just ONE analytic solution to the time-dependent Schrodinger Equation.

[IronHamster]

I have been trying to find an analytic solution to the time-dependent Schrödinger Equation. I plan to make a movie of the probability function as it changes over time, but I can't seem to find any analytic solution for the wave function.

Is it possible to solve the time-dependent Schrödinger Equation without approximation, or should I stop looking?

If it would be helpful, I can show what methods I have tried so far.

 

[Avodyne]

There are analytic solutions for either a free particle or for a harmonic oscillator with a wave function of the form exp[-a(t)x^2 - b(t)x], where a(t) and b(t) are particular complex functions of time.