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 Navier-Stokes 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.

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