The quantum canonical ensemble

The phase space Gamma of quantum mechanics can be viewed as the complex pro jective space CPn endowed with a Kahlerian structure given by the Fubini-St udy metric and an associated symplectic form. We can then interpret the Sch rodinger equation as generating a Hamiltonian dynamics on Gamma. Based upon the geometric structure of the quantum phase space we introduce the corres ponding natural microcanonical and canonical ensembles. The resulting densi ty matrix for the canonical Gamma-ensemble differs from the density matrix of the conventional approach. As an illustration, the results are applied t o the case of a spin one-half particle in a heat bath with an applied magne tic field. (C) 1998 American Institute of Physics. [S0022-2488(98)00212-6].