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Physica Scripta

N-mode linear-composite coordinate representation and its applications

Shi-Min Xu, Xing-Lei Xu, Jiang Ji-Jian, Hongqi Li

Published Jul 1, 2008• 6 citations
Publisher

Abstract

Using the technique of integration within an ordered product of operators, a unitary transformation matrix and N linear-composite coordinate operators are constructed for an N-particle system, and the complete and orthonormal common eigenvectors of the N linear-composite coordinate operators are examined. The N-mode linear-composite coordinate representation is proposed, and its application to a general N-mode coupling quantum harmonic system is studied for solving some dynamic problems.

DOI
10.1088/0031-8949/78/01/015015

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Using the technique of integration within an ordered product of operators, a unitary transformation matrix and N linear-composite coordinate operators are constructed for an N-particle system, and the complete and orthonormal common eigenvectors of the N linear-composite coordinate operators are examined. The N-mode linear-composite coordinate representation is proposed, and its application to a general N-mode coupling quantum harmonic system is studied for solving some dynamic problems.
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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.
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