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It is demonstrated that the probability density function, given by the squareof a quantum mechanical wavefunction that is a real-valued eigenvector of atime-independent, one-body Schroedinger equation, satisfies a compressible-flowgeneralization of the Bernoulli equation, where the mass density is theprobability density times the mass of the system; the pressure and velocityfields are defined by functions depending on the probability density, and thegradient and the Laplacian of the probability density, where there are twopossible directions of the velocity on a streamline. The velocity givendefinition implies a generalization of the steady-flow continuity equationwhere mass is not locally conserved. The gradient of the Bernoullian equationis demonstrated to be equivalent to the steady flow Euler equation for variablemass and irrotational flow. A speed of sound quadratic equation is obtainedfrom a spherical wave-pulse. One of the solutions indicates that the wave-pulsevelocity on a streamline is equal in magnitude but opposite in direction of thefluid velocity on the streamline. The other solution is the focus of attentionfrom that point on. It is proven that the extremums of the momentum per volumeon a streamline occur at points that are Mach 1 speed. The developed formalismis applied to a particle in a one-dimensional box, the ground and firstexcited-states of the one-dimensional harmonic oscillator, and the hydrogen 1sand 2s states. Some behavior is repeated in all the applications examined. Forexample, an antinode, a point of local-maximum density, has zero velocity andzero Mach speed on the streamline, while a node, a point of minimum density,has infinite velocity and Mach 2. In between the node and antinode is anextremum of the momentum, and Mach 1. (This is a short version of theabstract.)

The Fluid Dynamics of the One-Body Stationary States of Quantum Mechanics with Real Valued Wavefunctions