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.
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.
With the use of the general covariant matrix 10-dimensional Petiau-Duffin-Kemmer formalism in cylindrical coordinates exact solutions of the quantum-mechanical equation for a particle with spin 1 in the presence of an external homogeneous magnetic field are constructed. Three linearly independent types of solutions are separated; in each case the formula for the energy levels has been found.Within similar technique for the quantum-mechanical equation for a particle with spin 1 and additional intrinsic electromagnetic characteristics - polarizability, exact solutions are found in the presence of an external homogeneous magnetic field.