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Thermal Equilibrium Distribution of Wavefunctions

It is well known that in quantum theory, thermal equilibrium at inverse temperature β corresponds to the density matrix (1/Z) exp(−βH). But a density matrix that is not pure can arise from many different distributions of the wavefunction. We address in this paper the question which distribution of the wavefunction corresponds to thermal equilibrium, or, in other words, which distribution of the wavefunction represents the canonical ensemble. We propose here, and argue for, a specific candidate.