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- ItemMonotonicity properties of the quantum mechanical particle density(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2007) Kaiser, Hans-Christoph; Neidhardt, Hagen; Rehberg, JoachimAn elementary proof of the anti-monotonicity of the quantum mechanical particle density with respect to the potential in the Hamiltonian is given for a large class of admissible thermodynamic equilibrium distribution functions. In particular the zero temperature case is included.