Dear Prof. Adriano Orefice
Thank you for your kind reply. Allow me to answer your questions, but i am no mathematician, i was engineer who happens to be interested in some mathematical problems.
There was time (around 1997-2014) that I also took the same stand of you, that it is possible to consider non-probabilistic non-kopenhagen view of quantum mechanics. And i worked out some papers in the past using this view based correspondence between Navier-Stokes and Schrodinger. See also this webpage of John Bush from MIT:
Then, around 2014 i found some papers by Dr. George Shpenkov proving some inadequacies of Schrodinger equation. Especially he proves that Schrodinger equation in 3d case cannot predict anything in correspond to experimental facts. This is something that is neglected in most textbooks on QM, that is why many physicists nowadays hold the view that wave mechanics can predict "all" tests... This is unfounded assumption.
Around 2015-2017 i got to know Prof. Akira Kanda a logician/pure mathematics person, who shows convincingly that there are deep logical errors made by Schrodinger in deriving his equation. He started with relativistic De Broglie matter wave hypothesis combined with Hamilton-Jacobian to become a non-relativistic wave. In other words, he started with relativistic assumptions then he got a nonrelativistic assumption. That is why his equation is ill conceived, logically speaking.
So, getting back to your paper. You seem to be convinced that Helmholtz equation with some changes in k results in Schrodinger equation. It is nice exercise, but you forget the deep logical error as explained before. Therefore it is doubtful that wave mechanics, be it probabilistc or non-probabilistic case, cannot predict anything meaningfully, especially Wilsin chamber.
We need a classical mathematical model of Wilson experiment, and it is far from being complete.
Hopefully this reply may help you see the deep inherent problem within wave mechanics itself.
You can ask to Dr. George Shpenkov or Prof. Akira Kanda, as I also cc to them.
What do you think?
Your comments are welcome,