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A matrix which is constructed as the most general statistical description of the states of a many-particle quantum-mechanical system. The state of a quantum system is described by a normalized wave function ψ(x, t) [where x stands for all coordinates of the system, and t for the time], which satisfies the Schrödinger equation (1), where H is
In quantum statistics, one deals with an ensemble of N systems which have the same hamiltonian. If the αth member of the ensemble is in the state ψα in Eq. (4), the density matrix is defined as the ensemble average, Eq. (5).
an operator by means of which it is possible to calculate the average value of any physical quantity in quantum statistical mechanics and, in particular, in quantum mechanics. A density matrix describes a system’s state based on an incomplete set (incomplete in terms of quantum mechanics) of data on the system (seeMIXED STATE).