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Chinese Physics Letters

New Representation of Rotation Operator and Its Application

Shuai Wang, Jiang Ji-Jian, Hongqi Li

Published Jun 1, 2009• 5 citations
Publisher

Abstract

By employing the technique of integration within an ordered product of operators, we derive natural representations of the rotation operator, the two-mode Fourier transform operator and the two-mode parity operator in entangled state representations. As an application, it is proved that the rotation operator constructed by the entangled state representation is a useful tool to solve the exact energy spectra of the two-mode harmonic oscillators with coordinate-momentum interaction.

DOI
10.1088/0256-307x/26/6/060304

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We construct four linear composite operators for a two-particle system and give common eigenvectors of those operators. The technique of integration within an ordered product (IWOP) of operators is employed to prove that those common eigenvectors are complete and orthonormal. Therefore, a new two-mode intermediate momentum-coordinate representation which involves quantum entanglement for a two-particle system is proposed and applied to some two-body dynamic problems. Moreover, the pure-state density matrix |ξ 1 , ξ 2 〉 C,D C,D 〈ξ 1 , ξ 2 | is a Radon transform of Wigner operator.