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International Journal of Theoretical Physics

Spin-0 and Spin-1 Bosonic Particles Dynamics in $$(1+3)$$ Dimensions via the Relativistic DKP Equation with a Spatially-Dependent Exponential Mass Term

P. Mah Tsila, Sylvère Yannick Loemba Mouandza, A. Atangana Likéné, Serge Mbida Mbembe, E. Anemena Etoga, H. D. Yia Etolo, Germain Hubert Ben-Bolie

Published May 18, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.1007/s10773-026-06353-x

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Spin-0 and Spin-1 Bosonic Particles Dynamics in (1+3)(1+3)(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)(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}\textrm{Li}_{2}7Li2​ 7 Li 2 , Na2\textrm{Na}_{2}Na2​ Na 2 , and ScI. The energy spectra are computed for various quantum states ∣n,l,j⟩\left| n,l,j\right\rangle ∣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}\textrm{Li}_{2}7Li2​ 7 Li 2 , Na2\textrm{Na}_{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.
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 present the solution of the Duffin–Kemmer–Petiau equation for Manning–Rosen potential plus a ring-shaped-like potential in (1+3)-dimensional space–time for spin-one particles within the framework of an exponential approximation for the centrifugal term. We have used the Nikiforov–Uvarov method in our calculations. The radial wavefunction and the angular wavefunctions are expressed in terms of Jacobi polynomials. We have also represented some numerical results for the Manning–Rosen potential plus a ring-shaped-like potential.