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Common eigenstates of two particles’ center-of-mass coordinates and mass-weighted relative momentum

Common eigenstates of two particles’ center-of-mass coordinates and mass-weighted relative momentum We give the explicit form of the common eigenstate ‖ξ〉 of the center-of-mass coordinate μ 1 Q 1 + μ 2 Q 2 and the mass-weighted relative momentum μ 2 P 1 - μ 1 P 2 of two particles, which is more complicated than the common eigenstate of the other pair of commutative operators Q 2 - Q 1 and P 1 + P 2 . The orthonormal and completeness relation of ‖ξ〉 are investigated easily by virtue of the technique of integration within an ordered product of operators. The normally ordered squeezing operator for μ 1 Q 1 + μ 2 Q 2 and μ 2 P 1 - μ 1 P 2 is also derived by using the ‖ξ〉 representation. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review A American Physical Society (APS)

Common eigenstates of two particles’ center-of-mass coordinates and mass-weighted relative momentum

Physical Review A , Volume 51 (4) – Apr 1, 1995
4 pages

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Publisher
American Physical Society (APS)
Copyright
Copyright © 1995 The American Physical Society
ISSN
1094-1622
DOI
10.1103/PhysRevA.51.3343
Publisher site
See Article on Publisher Site

Abstract

We give the explicit form of the common eigenstate ‖ξ〉 of the center-of-mass coordinate μ 1 Q 1 + μ 2 Q 2 and the mass-weighted relative momentum μ 2 P 1 - μ 1 P 2 of two particles, which is more complicated than the common eigenstate of the other pair of commutative operators Q 2 - Q 1 and P 1 + P 2 . The orthonormal and completeness relation of ‖ξ〉 are investigated easily by virtue of the technique of integration within an ordered product of operators. The normally ordered squeezing operator for μ 1 Q 1 + μ 2 Q 2 and μ 2 P 1 - μ 1 P 2 is also derived by using the ‖ξ〉 representation.

Journal

Physical Review AAmerican Physical Society (APS)

Published: Apr 1, 1995

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