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Chinese Physics Letters

The s -Ordered Fock Space Projectors Gained by the General Ordering Theorem

Farid Shähandeh, M. R. Bazrafkan, Seyed Mahmoud Ashrafi

Published Sep 1, 2012• 1 citation
Publisher

Abstract

Employing the general ordering theorem (GOT), operational methods and incomplete 2-D Hermite polynomials, we derive the t-ordered expansion of Fock space projectors. Using the result, the general ordered form of the coherent state projectors is obtained. This indeed gives a new integration formula regarding incomplete 2-D Hermite polynomials. In addition, the orthogonality relation of the incomplete 2-D Hermite polynomials is derived to resolve Dattoli's failure.

DOI
10.1088/0256-307x/29/9/090301

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We introduce the general method of converting a given function of boson operators into its s -ordered form. We state and prove a theorem representing the fact that any ordered expansion of some operator function might be considered as the combinatorial problem of counting the number of contractions. In this way, we reduce the general ordering problem of boson operators into a purely combinatorial one. We show the applications of the theorem through some generic examples from quantum optics, namely ordering of the Fock space projectors, together with some simple extensions of the previously given quantum optical lemmas.
In this paper, by virtue of the entangled state representation we concisely derive some new operator identities regarding to two-variable Hermite polynomial (TVHP). By them and the technique of integration within an ordered product (IWOP) of operators we further derive new generating function formulas of TVHP. They are useful in quantum optical theoretical calculations. It is seen from this work that by combining the IWOP technique and quantum mechanical representations one can derive some new integration formulas even without really performing the integration.
By virtue of the entangled state representation we concisely derive some new operator identities with regard to the two-variable Hermite polynomial (TVHP). By them and the technique of integration within an ordered product (IWOP) of operators we further derive new generating function formulas of the TVHP. They are useful in quantum optical theoretical calculations. It is seen from this work that by combining the IWOP technique and quantum mechanical representations one can derive some new integration formulas even without really performing the integration.