# Psi from probability density

1. Aug 7, 2011

### 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?

2. Aug 8, 2011

### 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.

3. Aug 8, 2011

### 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.