Mixed State

mixed state

[¦mikst ¦stāt] (solid state physics) The state of a superconductor at magnetic field strengths between the lower critical field and the upper critical field, at which the magnetic field is partially excluded from the superconductor but penetrates it as microscopic filaments called fluxoids.

Mixed State

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) w_i and the average values Ā_i of the quantity A in the pure states ψ_i:

where Ā_i = ∫ ψ*_i(x) Âψ_i, (x) dx and ψ_i (x) is the wave function in the coordinate representation (the total probability Σw_i = 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.

REFERENCE

Davydov. A. S. Kvantovaia mekhanika, 2nd ed. Moscow, 1973.

D. N. ZUBAREV

单词	mixed state
释义	Mixed State mixed state [¦mikst ¦stāt] (solid state physics) The state of a superconductor at magnetic field strengths between the lower critical field and the upper critical field, at which the magnetic field is partially excluded from the superconductor but penetrates it as microscopic filaments called fluxoids. Mixed State 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) w_i and the average values Ā_i of the quantity A in the pure states ψ_i: where Ā_i = ∫ ψ_i(x) Âψ_i, (x) dx and ψ_i* (x) is the wave function in the coordinate representation (the total probability Σw_i = 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. REFERENCE Davydov. A. S. Kvantovaia mekhanika, 2nd ed. Moscow, 1973. D. N. ZUBAREV
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