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Psi from probability density

  1. Aug 7, 2011 #1
    I have a 3 dimensional orbital-specfic electron density function ( |[itex]\psi[/itex](r)|2 ) for all relevant r values. How would I go about finding the corresponding [itex]\psi[/itex](r)? I know it would be something related to a Fourier transform, I'm just unsure about how to go about performing it in mathematica or matlab. Can anyone give me any pointers?
  2. jcsd
  3. Aug 8, 2011 #2


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    You can't. Probability density carries less information than wave function. Many wave functions may lead to the same probability density. Even Fourier can't help.
  4. Aug 8, 2011 #3


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    If it's as simple as you're making it sound, with no spin dependence or (θ,φ) dependence, just r dependence, then the wavefunction ψ for a nondegenerate stationary state can always be chosen to be real. (Proof: by time-reversal invariance ψ* is also a solution, so if there's only one solution then ψ = ψ*.) So if that's the case, just take the square root.
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