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Physica Scripta

The q -deformed spin-one DKP oscillator in 1 + 2 dimensions

YASSINE CHARGUI, A. Dhahbi, Abdelmalek Boumali

Published Jul 17, 2025• 1 citation

Abstract

Abstract We consider a q -deformed extension of the Duffin–Kemmer–Petiau oscillator (DKPO) for spin-one bosons in two spatial dimensions. The corresponding problem is easily solved algebraically after realization of the q -deformed algebra in terms of operators of the ordinary Bose algebra. For states associated with the spin-projection numbers ± 1 an equivalent equation in Hamiltonian form is obtained where the Hamiltonian is pseudo-Hermitian, supporting the idea that pseudo-Hermitian models are physically relevant. Then, using the spectral method, we derived the exact expressions for the corresponding metric operator and Hermitian Hamiltonian in closed forms Notably, this Hamiltonian is found to be diagonal, thus implying that the transformation we applied to the pseudo-Hermitian Hamiltonian to work it out is a Foldy-Wouthuysen transformation.

DOI: 10.1088/1402-4896/adf148

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Abstract We consider a q -deformed extension of the Duffin–Kemmer–Petiau oscillator (DKPO) for spin-one bosons in two spatial dimensions. The corresponding problem is easily solved algebraically after realization of the q -deformed algebra in terms of operators of the ordinary Bose algebra. For states associated with the spin-projection numbers ± 1 an equivalent equation in Hamiltonian form is obtained where the Hamiltonian is pseudo-Hermitian, supporting the idea that pseudo-Hermitian models are physically relevant. Then, using the spectral method, we derived the exact expressions for the corresponding metric operator and Hermitian Hamiltonian in closed forms Notably, this Hamiltonian is found to be diagonal, thus implying that the transformation we applied to the pseudo-Hermitian Hamiltonian to work it out is a Foldy-Wouthuysen transformation.

Spin-0 and Spin-1 Bosonic Particles Dynamics in

(1+3)

Dimensions via the Relativistic DKP Equation with a Spatially-Dependent Exponential Mass Term

Abstract The Duffin-Kemmer-Petiau (DKP) equation is a relativistic wave equation governing the dynamics of spin-0 and spin-1 bosonic particles. In this work, we study the

(1+3)

( 1 + 3 ) -dimensional DKP equation with a spatially dependent mass under a modified deformed exponential type potential. Using the framework of supersymmetric quantum mechanics, we derive approximate analytical solutions. A novel extension of the Pekeris approximation is introduced to treat the centrifugal barrier, enabling the complete determination of the energy spectrum. The non-relativistic limit of the DKP equation is obtained via an established transformation technique. The model is applied to diatomic molecules including lithium hydride (LiH), hydrogen chloride (HCl),

^{7}\textrm{Li}_{2}

7 Li 2 ,

\textrm{Na}_{2}

Na 2 , and ScI. The energy spectra are computed for various quantum states

\left| n,l,j\right\rangle

n , l , j using both relativistic and non-relativistic expressions. For LiH and HCl, where experimental data are scarce, our results show strong agreement with earlier theoretical predictions. For

^{7}\textrm{Li}_{2}

7 Li 2 ,

\textrm{Na}_{2}

Na 2 , and ScI, the calculated energies align excellently with available experimental data. The proposed framework provides a reliable and analytically tractable tool for studying bosonic systems with position-dependent effective masses.

The recently introduced by us, two- and three-parameter (p, q)- and (p, q, [Formula: see text])-deformed extensions of the Heisenberg algebra were explored under the condition of their direct link with the respective (nonstandard) deformed quantum oscillator algebras. In this paper, we explore certain Hermitian Hamiltonians build in terms of non-Hermitian position and momentum operators obeying definite [Formula: see text](N)-pseudo-hermiticity properties. A generalized nonlinear (with the coefficients depending on the particle number operator N) one-mode Bogoliubov transformation is developed as main tool for the corresponding study. Its application enables to obtain the spectrum of “almost free” (but essentially nonlinear) Hamiltonian.