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Chinese Physics Letters

Normally Ordered Expansion of the Even-Power of the Radial Coordinate Operator

Fan Hong‐Yi

Published Oct 10, 2001• 5 citations
Publisher

Abstract

By virtue of the technique of integration within an ordered product of operators we derive the concise normally ordered expansion of the even-power of the radial coordinate operator via the equation = ∫ d 3 x | x ⟩⟨ x | r , where | x ⟩ is the three-dimensional coordinate eigenvector, and r = ( x 2 + y 2 + z 2 ) 1/2 . The application to perturbation theory is briefly discussed.

DOI
10.1088/0256-307x/18/11/301

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By virtue of the technique of integration within an ordered product of operators we derive the concise normally ordered expansion of the even-power of the radial coordinate operator via the equation = ∫ d 3 x | x ⟩⟨ x | r , where | x ⟩ is the three-dimensional coordinate eigenvector, and r = ( x 2 + y 2 + z 2 ) 1/2 . The application to perturbation theory is briefly discussed.
In this paper by virtue of the technique of integration within an ordered product (IWOP) of operators and the intermediate coordinate-momentum representation in quantum optics, we derive the normal ordering and antinormal ordering products of the operator ( fQ + gP ) n when n is an arbitrary integer. These products are very useful in calculating their matrix elements and expectation values and obtaining some useful mathematical formulae. Finally, the applications of some new identities are given.