A serendipity event in 1975 led to the discovery of a complex mapping that
transformed the two dimensional time dependent Schroedinger equation for a
charged particle in an electromagnetic field into a complex differential
equation. When the imaginary component was separated, it was exactly of the
form of the NavierStokes vorticity equation for a compressible VISCOUS (!)
fluid. Click here
The transformation was not equivalent to the Magdelung transformation that leads
to a nonviscous Eulerian fluid. At that time I was not conversant with the
Bohm view of quantum mechanics, and the concept of a "pilot" wave that depended
upon a gradient field (or potential function). However, the complex mapping
mentioned above effectively extends the Bohm approach to pilot fields that are
not represented by perfect differentials. Indeed, the absolute square of the
wave function, through the NavierStokes construction, is not a position
probability, but is precisely the square of the vorticity distribution in the
NavierStokes fluid.
