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International Journal of Theoretical Physics

Common Eigenvectors of Four Particles’ Compatible Observables

Shi-Min Xu, Xing-Lei Xu, Hongqi Li

Published Mar 4, 2008• 4 citations
Publisher
DOI
10.1007/s10773-008-9677-2

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We construct 2N operators for a N-particle system, namely one center-of-mass coordinate operator, N-1 relative coordinate operators, one total momentum operator and N-1 mass-weighted relative momentum operators, and give common eigenvectors of N compatible observables [Formula: see text], which are composed of N particles' coordinate [Formula: see text] and momentum [Formula: see text]. By compatible, we mean such observables can be simultaneously determined. Using the technique of integration within an ordered product of operators (IWOP), we prove that the common eigenvectors are complete and orthonormal, and hereby qualified for making up a representation. This new representation can be applied to solving some dynamic problems in quantum mechanics.