量子力学与实验7.pdf

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量子力学与实验7.pdf

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CN Chapter 7 CT Selected Topics A 7.1 Quantum Statistics Quantum statistical mechanics is the branch of physics dealing with systems in mixed states; it is the quantum analogue of classical statistical mechanics. It should be noted that sta- tistics enters at two levels in quantum statistical mechanics: ﬁrst, because of the statistical interpretation of the wave function and second, because of our incomplete knowledge of dynamical state of the system. B 7.1.1 Density Operator and Ensembles Question: How to describe quantum mechanically an ensemble of physical systems for which, say ωα =60% are characterized by |α and the remaining ωβ =40% are characterized by some other ket |β . 205 CHAPTER 7 – MANUSCRIPT Example: a general state for S=1/2 system |α = c+ |+ + c− |− which characterizes a state ket whose spin is pointing some deﬁnite direction. We should not confuse the probability weight of the states |+ and |− , ω ± , and |c± |2 . Ensemble average and density operator. Pure ensemble: |α Mixed ensembles: (1) ω 1 α (2) ω2 α (3) ω3 α . . . .