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Can you graph complex #'s in Mathematica?

  1. Oct 12, 2004 #1
    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. jcsd
  3. Feb 5, 2009 #2
    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).
     
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