Can you graph complex #'s in Mathematica?

1. Oct 12, 2004

DharmaBum

I want to evolve a 1 dimensional wavefunction forward in time. It is an eigenstate of the Hamiltonian, so its time dependence is e^(-i * w * t). Is there a way to graph it on the x axis and animate it to show how it rotates through the real and complex planes?
This is how I have tried it; it doesnt work.
Plot3D[ψ[x, 100, .1, 1, t], {x, 0, 100}, {t, 0, 600}, AxesLabel -> {"
Real", "x", "\[ImaginaryI]"}]

2. Feb 5, 2009

gold2.718

ParametricPlot3D to the rescue!
Manipulate[
ParametricPlot3D[{Sin[Pi*q/2]*Cos[-Pi*t/50],
Sin[Pi*q/2]*Sin[-Pi*t/50], q}, {q, 0, 2},
AxesLabel -> {"Re", "Im", "x"}, PlotStyle -> {Thick, Red},
PlotRange -> {{-1.0, 1.0}, {-1.0, 1.0}, {0.0, 2.0}}], {t, 0, 100, 0.1}]
This will play the ground state of an infinite square well forward in time. If you use the option, ViewPoint -> {0, Infinity, 0}, you will see the standard real plot.
I have put together a Mathematica notebook which shows some of the features you can show (such as superposition).