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NATO ASI series. Series B : Physics

The Dynamics of the Pure State Density Matrix for Hamiltonian Systems

Edward R. Pike, Sarben Sarkar, J.S. Satchell

Published Jan 1, 1987• 0 citations
Publisher
DOI
10.1007/978-1-4899-5382-7_8

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An algebraic procedure to find extremal density matrices for the expectation value of a finite Hamiltonian matrix is established. The extremal density matrices for pure states provide a complete description of the system, that is, its corresponding energy spectrum and projectors. For density matrices representing mixed states, one gets the most probable eigenstates that yield extremal mean values of the energy. The procedure uses mainly the stationary solutions of the von Neumann equation of motion, the orbits of the Hamiltonian, and the positivity conditions of the density matrix. The method is illustrated for matrix Hamiltonians of dimensions d = 2 and d = 3.