Can you graph complex #'s in Mathematica?

[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 doesn't work.
Plot3D[ψ[x, 100, .1, 1, t], {x, 0, 100}, {t, 0, 600}, AxesLabel -> {"
Real", "x", "\[ImaginaryI]"}]

 

[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 http://spot.colorado.edu/~goldy/Mathematica/TimeDependentWaveFunction.nb" which shows some of the features you can show (such as superposition).

 

[oswaler]

Yes, it is possible to graph complex numbers in Mathematica. In fact, Mathematica has built-in functions specifically for working with complex numbers, such as ComplexPlot and ComplexListPlot. These functions allow you to plot the real and imaginary components of a complex number separately or together.

As for animating the time evolution of a 1-dimensional wavefunction, you can use the Manipulate function in Mathematica to create an interactive animation. First, you would define your wavefunction as a function of both x and t, using the exponential time dependence described in the question. Then, you can use Manipulate to vary the value of t and see how the wavefunction changes over time.

Here is an example code that you can use as a starting point:

Manipulate[ComplexPlot[ψ[x, 100, .1, 1, t], {x, 0, 100}, AxesLabel -> {"Real", "Imaginary"}, PlotRange -> All], {t, 0, 600}]

This code assumes that you have defined the function ψ with the appropriate parameters. You can adjust the parameters and the range of the plot to suit your specific needs.

I hope this helps and good luck with your research!