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arXiv:1607.06169 · The European Physical Journal Plus

SU(1,1) solution for the Dunkl oscillator in two dimensions and its coherent states

M. Salazar–Ramírez, D. Ojeda-Guillén, R. D. Mota, V. D. Granados

Published Jan 1, 2017• 55 citations
arXivHTMLPDF
DOI
10.1140/epjp/i2017-11314-3

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We investigate the $d$-dimensional Dunkl--Klein--Gordon equation for a scalar particle within an algebraic framework. By employing Schrödinger factorization, we construct the generators of the $\mathfrak{su}(1,1)$ algebra and establish the associated symmetry of the radial sector. The corresponding energy spectra are derived from unitary irreducible representations, and the Sturmian radial bases are obtained analytically. We analyze the $d$-dimensional Dunkl--Klein--Gordon oscillator and the bound-state sector of the $d$-dimensional Dunkl--Klein--Gordon equation with a Dunkl--Coulomb-like potential. Furthermore, $\mathrm{SU}(1,1)$ coherent states are constructed and their time evolution is analyzed, revealing a characteristic radial oscillation behavior. The results show that the Dunkl deformation modifies the spatial and spectral structure of the system and, in the oscillator sector, introduces explicit parity-dependent energy shifts while preserving the underlying radial algebraic dynamics.

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We investigate the ddd-dimensional Dunkl--Klein--Gordon equation for a scalar particle within an algebraic framework. By employing Schrödinger factorization, we construct the generators of the su(1,1)\mathfrak{su}(1,1)su(1,1) algebra and establish the associated symmetry of the radial sector. The corresponding energy spectra are derived from unitary irreducible representations, and the Sturmian radial bases are obtained analytically. We analyze the ddd-dimensional Dunkl--Klein--Gordon oscillator and the bound-state sector of the ddd-dimensional Dunkl--Klein--Gordon equation with a Dunkl--Coulomb-like potential. Furthermore, SU(1,1)\mathrm{SU}(1,1)SU(1,1) coherent states are constructed and their time evolution is analyzed, revealing a characteristic radial oscillation behavior. The results show that the Dunkl deformation modifies the spatial and spectral structure of the system and, in the oscillator sector, introduces explicit parity-dependent energy shifts while preserving the underlying radial algebraic dynamics.