On Interbasis Expansion for Isotropic Oscillator on Two-Dimensional Sphere
Ye. M. Hakobyan, G. S. Pogosyan
备注：
9 pages, LaTex
发表信息：
Proc., II International Workshop "Lie Theory and Its Applications in Physics", (Clausthal, August 1997); eds. H.-D. Doebner, V.K. Dobrev and J. Hilgert, (World Sci, Singapore, 1998, ISBN 981-02-3539-9) pp. 243-251
In this article we analyze the isotropic oscillator system on the two-dimensional sphere in the spherical systems of coordinates. The expansion coefficients for transitions between three spherical bases of the oscillator are calculated. It is shown that these coefficients are expressed through the Clebsch-Gordan coefficients for SU(2) group analytically continued to real values of their argument.
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Exactly solvable model of the quantum isotropic three-dimensional singular oscillator in the relativistic configurational $\vec r$-space is proposed. We have found the radial wavefunctions, which are expressed through the continuous dual Hahn polynomials and energy spectrum for the model under consideration. It is shown that they have the correct non-relativistic limits.
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We introduce a new method for constructing squeezed states for the 2D isotropic harmonic oscillator. Based on the construction of coherent states in [1], we define a new set of ladder operators for the 2D system as a linear combination of the x and y ladder operators and construct the SU(2) coherent states. The new ladder operators are used for generalizing the squeezing operator to 2D and the SU(2) coherent states play the role of the Fock states in the expansion of the 2D squeezed states. We discuss some properties of the 2D squeezed states.
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Magic numbers predicted by a 3-dimensional q-deformed harmonic oscillator with Uq(3) > SOq(3) symmetry are compared to experimental data for alkali metal clusters, as well as to theoretical predictions of jellium models, Woods--Saxon and wine bottle potentials, and to the classification scheme using the 3n+l pseudo quantum number. The 3-dimensional q-deformed harmonic oscillator correctly predicts all experimentally observed magic numbers up to 1500 (which is the expected limit of validity for theories based on the filling of electronic shells), thus indicating that Uq(3), which is a nonlinear…
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