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Communications in Theoretical Physics

Coherent State Representation for a Kind of Operator Disentangling Formulae

Fan Hong‐Yi, Zou Hui, Hui Wang

Published Oct 30, 2000• 0 citations
Publisher

Abstract

We derive a kind of operator disentangling formulae and their coherent state representation by virtue of the correspondence between symplectic transformations and their quantum mechanical images. The application of the formulae in calculating Feynman transformation matrix elements is discussed.
DOI
10.1088/0253-6102/34/3/541

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We present a novel method for deriving some new quantum operator formulas by carrying out the integrations within a normal product symbol. The idea underlying this method is combining the properties of normal product and of coherent state together. For example, we can deduce operator ordering theorems, the Fujiwara formula, and some disentangling theorems simply and directly. By means of this method we also get the explicit operator form and coherent state form for the Wigner function with these new forms, the wigner function's eigenstate is found and its zero point value property is discussed. Furthermore some famous quantum unitary transformations and the transformed matrix element for functional obtained conveniently. integral may be also
Feynman’s disentangling theorem is applied to noncommuting operators in the problem of quantum parametric oscillator, which is mathematically equivalent to the problem of SU (1, 1) pseudospin rotation. The number states of the oscillator correspond to unitary irreducible representations of the SU (1, 1) group. Feynman disentangling is combined with group-theoretic arguments to obtain simple analytical formulas for the matrix elements and transition probabilities between the initial and final states of the oscillator. Feynman disentangling of time evolution operators is also discussed for an atom or ion interacting with a laser field and for a model Hamiltonian possessing the “ hidden” symmetry of the hydrogen atom.