Are there any speculations on where wave functions come from?

Question

How do wave functions arise?

Are there any models, also speculative, on where wave functions come from?

Did anybody ever suggest a mechanism for their origin?

Such a model would have to get around the various hidden variable theorems. I looked through Google Scholar but did not find anything. 

Answer 1

I am not an expert in the history of science, but historically the observation of the diffraction of "particles" appears to be of high significance. Diffraction is a phenomenon characteristic of waves. The obvious question then was what the wave equation for these waves is, leading to the Schrödinger equation.

As for "models ... where wave functions come from" and "a mechanism for their origin": Such models or mechanisms have to be based on something. Here the question is what constitutes an acceptable basis.