## Download On the calculation of time correlation functions by Berne B.J., Harp G.D. PDF

By Berne B.J., Harp G.D.

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It is a convenient fiction to assert that every Hermitian operator symbolizes a physical quantity, and that every unit vector symbolizes a state. Then the expectation value of property in the state ¥ X is given by In particular, the probability of observing the values a1 in an A-measurement performed on sys- tems in the state 2,5 ¥ is UNITARY TRANSFORMATIONS The automophisms of the unitary geometry of states are produced by the unitary transformations THE GEOMETRY OF STATES 41 applied to every vector and operator, where the unitary operator U obeys All algebraic relations and adjoint connections among vectors and operators are preserved by this transformation.

2 RECONSTRUCTION OF THE MEASUREMENT ALGEBRA THE GEOMETRY OF STATES 33 The characteristics of the measurement operators M(a" of the *F f b') and * can now be derived from those symbols. 12). 6) show that the only significant products those not identically zero — ¥

70), we learn that or which expresses the fixed numerical values of the. transformation function Indeed, the latter is not an independent condition on transformation functions but is implied by the composition property and the requirement that transformation functions, as matrices, be nonsingular. 11 <§W are Hermitian. 33) to write the probability formula as the expectation value becomes 26 QUANTUM KINEMATICS AND DYNAMICS where the operator A is The correspondence thus obtained between operators and physical quantities is such that a function f(A) of the property A is assigned the operator £{A) , and the operators associated with a complete set of compatible physical quantities form a complete set of commuting Hermitian operators.