An exact complex mapping of the wave function has been found, which, when
followed by a separation into real and imaginary parts, transforms the
Schroedinger equation for a charged particle interacting with an electromagnetic
field into two partial differential systems. The first partial differential
system is exactly the evolutionary equation for the vorticity of a compressible,
viscous NavierStokes fluid. The second system is related to the Beltrami
equation defining a minimal surface in terms of the kinetic and potential
energy. The absolute square of the wave function is exactly the vorticity
distribution (including topological vorticity defects) in a fluid with a
viscosity coefficient, nu = hm/2pi. This cohomological, but classical,
interpretation of the wave function offers an alternative to the Copenhagen
dogma. The connection with minimal surface theory implies that there should
exist characteristic sets of tangential discontinuities among the solutions to
the Schroedinger equation.
