I'm currently doing a mathematica for physicists course and am struggling to solve a problem we were given!
I'm supposed to define an initial wavefunction in a harmonic oscillator (displaced, stretched or compressed ground state for example). Then I should propagate the wave function in time and use NDSolve to solve the resulting PDE. To keep the expressions simple, constants are set to 1.
Now I really don't know how to use mathematica well yet so I'm struggling to start this exercise. I first define an initial wavefunction.
ψinit[x_] := Exp[-x^2/2]
Then to propagate in time I can multiply it by the time evolution:
ψinit[x_, t_] := ψinit[x] Exp[-I*E_n*t/ħ]
But I do not understand how I'm supposed to get a PDE from this that I can solve.
Any help appreciated :) Thanks