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Equations of motion for superfluids.

To the principles of least action and minimum error, for determining the time evolution of the parameters in a variational wave function, we add a third: continuous collapse dynamics. In this formulation, exact time evolution is applied for an infinitesimal time and is followed by projection of the state back into the variational manifold (``collapse''). All three principles lead to the same equations of motion when applied to complex parameters but take two distinct forms when the parameters are real. As an application of these principles, we study the time evolution of two variational wave functions for superfluids. The first wave function, containing real parameters, was considered by Kerman and Koonin [Ann. Phys. (N.Y.) 100, 332 (1976)] and leads to the Euler equation in the hydrodynamic limit. The equation for our second wave function, a coherent state of Feynman excitations with complex parameters, has essentially the same hydrodynamic limit. The latter wave function, however, has a significant advantage in that the equation it generates is useful and meaningful on a microscopic scale as well.