How Can You Determine the Wavefunction ψ(r) from Electron Density |\psi(r)|^2?

[digermane]

I have a 3 dimensional orbital-specfic electron density function ( |\psi(r)|² ) for all relevant r values. How would I go about finding the corresponding \psi(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?

 

[xts]

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.

 

[Bill_K]

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.