Communications in Theoretical Physics

Effective Way of Finding Common Eigenvectors of Center-of-Mass Coordinate and Mass-Weighted Relative Momenta of Multi-Partite via IWOP Technique

Shuguang Liu, Fan Hong-Yi

Published Mar 1, 2010• 1 citation

Abstract

We present a convenient approach to finding multi-partite entangled state with continuum variables, which is the common eigenvectors of center-of-mass coordinate and mass-weighted relative momenta, by decomposing the normally ordered Gaussian-form operator expressing the completeness relation which is constructed by analyzing the eigenvector equations. The whole derivation is based on the technique of integration within an ordered product of operators.

DOI: 10.1088/0253-6102/53/3/10

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Communications in Theoretical Physics

Effective Way of Finding Common Eigenvectors of Center-of-Mass Coordinate and Mass-Weighted Relative Momenta of Multi-Partite via IWOP Technique

Shuguang Liu, Fan Hong-Yi

Published Mar 1, 2010• 1 citation

Publisher

Abstract

DOI: 10.1088/0253-6102/53/3/10

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理论物理通讯：英文版Jan 1, 20100 citations

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We give the explicit form of the common eigenstate \ensuremath{\Vert}\ensuremath{\xi}〉 of the center-of-mass coordinate ${\mathrm{\ensuremath{\mu}}}_{1}$

{\mathit{Q}}_{1}

+${\mathrm{\ensuremath{\mu}}}_{2}$

{\mathit{Q}}_{2}

and the mass-weighted relative momentum ${\mathrm{\ensuremath{\mu}}}_{2}$

{\mathit{P}}_{1}

-${\mathrm{\ensuremath{\mu}}}_{1}$

{\mathit{P}}_{2}

of two particles, which is more complicated than the common eigenstate of the other pair of commutative operators

{\mathit{Q}}_{2}

{\mathit{Q}}_{1}

and

{\mathit{P}}_{1}

{\mathit{P}}_{2}

. The orthonormal and completeness relation of \ensuremath{\Vert}\ensuremath{\xi}〉 are investigated easily by virtue of the technique of integration within an ordered product of operators. The normally ordered squeezing operator for ${\mathrm{\ensuremath{\mu}}}_{1}$

{\mathit{Q}}_{1}

+${\mathrm{\ensuremath{\mu}}}_{2}$

{\mathit{Q}}_{2}

and ${\mathrm{\ensuremath{\mu}}}_{2}$

{\mathit{P}}_{1}

-${\mathrm{\ensuremath{\mu}}}_{1}$

{\mathit{P}}_{2}

is also derived by using the \ensuremath{\Vert}\ensuremath{\xi}〉 representation.