More than twenty years ago I had an idea. Riccati Quantum Mechanics. I was inspired by Bogdan Mielnik's students at CINVESTAV. I dawdle, and now other people have made progress in that direction: Marco Antonio Reyes, and Sergey V. Ershkov.
I feel I have to make out for lost time. Why am I interested in this, anyway?
Then it was a technical issue. I could solve differential equations in new ways, now I believe this interest is more general.
As I write in this blog, I see a new scientific method. This new method requires new interpretations of Quantum Mechanics, and even though, Riccati issues seem only technical. I hope I can make my point stronger this way.
As Bogdan showed, given a quantum spectrum, there are several quantum forces producing those observable numbers. Force is not a physical quantity in this new view, forces are devices to get good fits. What I care about is the fit, not the explanation. I see my point as neo-machian.
Maybe there are atoms, maybe there are fields, maybe there are forces, all I know is that there are good fits.
Gauss becomes the Prince of Science in my book.
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