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The recent remarkable developments in quantum optics, mesoscopic and coldatom physics have given reality to wave functions. It is then interesting toexplore the consequences of assuming ensembles over the wave functions simplyrelated to the canonical density matrix. In this note we analyze a previouslyintroduced distribution over wave functions which naturally arises consideringthe Schroedinger equation as an infinite dimensional dynamical system. Inparticular, we discuss the low temperature fluctuations of the quantumexpectations of coordinates and momenta for a particle in a double wellpotential. Our results may be of interest in the study of chiral molecules.Comment: 6 pages, 2 figures, contribution to Quantum Jumps Conferenc

On the statistics of quantum expectations for systems in thermal equilibrium