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.
We develop the Duffin–Kemmer–Petiau (DKP) approach in the phase-space picture of quantum mechanics by considering DKP algebras in a Galilean covariant context. Specifically, we develop an algebraic calculus based on a tensor algebra defined on a five-dimensional space which plays the role of spacetime background of the non-relativistic DKP equation. The Liouville operator is determined and the Liouville–von Neumann equation is written in two situations: the free particle and a particle in an external electromagnetic field. A comparison between the non-relativistic and the relativistic cases is commented.
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),
7Li2 7 Li 2 ,
Na2 Na 2 , and ScI. The energy spectra are computed for various quantum states
∣n,l,j⟩ 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
7Li2 7 Li 2 ,
Na2 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.