mixed state[¦mikst ¦stāt]
A mixed state of a quantum-mechanical system is a state that, in contrast to a pure state, is not described by a wave function. In a mixed state, the complete set of independent physical quantities that define the state of the system is not specified. Instead, only the quantities w1, w2, … are defined: these are the probabilities of finding the system in different quantum states described by the wave functions ψ1, ψ2,….
The average value Ā of some physical quantity A (to which there corresponds the operator A) is defined in the mixed state as the sum of the products of the probabilities (statistical weights) wi and the average values Āi of the quantity A in the pure states ψi:
where Āi = ∫ ψ*i(x) Âψi, (x) dx and ψi (x) is the wave function in the coordinate representation (the total probability Σwi = 1). In the mixed state, states are not superposed: different quantum states do not interfere with each other, since in determining the average value of A average values rather than wave functions are added.
A nonpolarized beam of particles or a gas in a thermostat are examples of the mixed state. The concept of the mixed state plays an important role in quantum statistics and in measurement theory in quantum mechanics.
REFERENCEDavydov. A. S. Kvantovaia mekhanika, 2nd ed. Moscow, 1973.
D. N. ZUBAREV