I know about and believe to understand the general wave equation based Kirchhoff diffraction formula, which in the Fraunhofer limit leads to a farfield complex wave function by Fourier transforming the complex wave function of the incident beam in the aperture.
I believe it should be possible to describe this phenomenon through only the density (wavefunction squared) and probability current (quantum mechanically). These two should be able to provide the phase and amplitude information necessary to interfere something.
What I'm looking for is a "hydrodynamic" theory of diffraction and/or interference, which I think should be very well possible.
Has this been done before? Am I barking up a wrong tree?