Abstract
The invariance under canonical transformations of the fundamental Cartesian coordinates and conjugate momenta commutators is used to show that the state labeling schemes of Elliott and Moshinsky are applicable to the case of many particles in an anisotropic harmonic oscillator potential. The relationship of the states obtained to the group theoretically equivalent isotropic harmonic oscillator states is investigated. The results reveal explicitly the collective nature of the particle-hole structure induced by the deformation.NUCLEAR STRUCTURE Theory, many particle states, anisotropic (deformed) harmonic oscillator, relation to isotropic harmonic oscillator states.
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