EXOTIC REPRESENTATIONS OF THE ISOTROPIC HARMONIC OSCILLATOR

1998 ◽  
Vol 13 (19) ◽  
pp. 3347-3360
Author(s):  
LUIS J. BOYA ◽  
ERIC CHISOLM ◽  
S. M. MAHAJAN ◽  
E. C. G. SUDARSHAN

We contruct and study a continuous family of representations of the N-dimensional isotropic harmonic oscillator (N≥2) which are not unitarily equivalent to the standard one. We explain why such representations exist and we investigate their simpler properties: the spectrum of the Hamiltonian (which contains nonstandard values), the form of the energy eigenfunctions, and their behavior under the ladder operators. Various symmetry and dynamical groups (e.g. the rotation group) which are valid on the standard representation are not implemented on the new ones. We comment very briefly on the prospects of observing these representations experimentally.

2014 ◽  
Vol 29 (21) ◽  
pp. 1444015
Author(s):  
Peter Minkowski

The present lecture is devoted to embedding the approximate genuine harmonic oscillator structure of valence [Formula: see text] mesons and in more detail the qqq configurations for u, d, s flavored baryons in QCD for three light flavors of quark. It includes notes, preparing the counting of "oscillatory modes of N fl = 3 light quarks, u, d, s in baryons," using the [Formula: see text] broken symmetry classification, extended to the harmonic oscillator symmetry of 3 paired oscillator modes. [Formula: see text] stands for the space rotation group generated by the sum of the 3 individual angular momenta of quarks in their c.m. system. The oscillator extension to valence gauge boson states is not yet developed to a comparable level.


2019 ◽  
Vol 17 (02) ◽  
pp. 2050021
Author(s):  
H. Fakhri ◽  
S. E. Mousavi Gharalari

We use the recursion relations of the continuous [Formula: see text]-Hermite polynomials and obtain the [Formula: see text]-difference realizations of the ladder operators of a [Formula: see text]-oscillator algebra in terms of the Askey–Wilson operator. For [Formula: see text]-deformed coherent states associated with a disc in the radius [Formula: see text], we obtain a compact form in [Formula: see text]-representation by using the generating function of the continuous [Formula: see text]-Hermite polynomials, too. In this way, we obtain a [Formula: see text]-difference realization for the [Formula: see text]-oscillator algebra in the finite interval [Formula: see text] as a [Formula: see text]-generalization of known differential formalism with respect to [Formula: see text] in the interval [Formula: see text] of the simple harmonic oscillator.


1997 ◽  
Vol 12 (10) ◽  
pp. 685-690 ◽  
Author(s):  
Ion I. Cotăescu

A family of geometric models of quantum relativistic rotating oscillator is defined by using a set of one-parameter deformations of the static (3+1) de Sitter or anti-de Sitter metrics. It is shown that all these models lead to the usual isotropic harmonic oscillator in the nonrelativistic limit, even though their relativistic behavior is different. As in the case of the (1+1) models,1 these will have even countable energy spectra or mixed ones, with a finite discrete sequence and a continuous part. In addition, all these spectra, except that of the pure anti-de Sitter model, will have a fine-structure, given by a rotator-like term.


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