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Approximate analytical solutions of Duffin–Kemmer–Petiau equation are obtained for a vector Hulthén potential. The solutions are reported for any J-state using an elegant approximation and methodology of supersymmetry quantum mechanics.

In this paper, the behavior of a Duffin–Kemmer–Petiau (DKP) boson particle in the presence of a harmonic energy-dependent interaction, under the influence of an external magnetic field is precisely studied. In order to exactly solve all equations in commutative (C), non-commutative (NC) and non-commutative phase (NCP) frameworks, the Nikiforov–Uvarov (NU) powerful exact approach is employed. All these attempts end up with solving their quartic equations, trying to find and discuss on their discriminant function $\mathrm{\Delta }$, in a unique way which has never been discussed for any boson in any other research, especially for the boson ${\pi }^{-}$ on which, we have been exclusively concerned. We finally succeeded to obtain the exact energy spectrums and wave functions under the effects of NC and NCP parameters and energy-dependent interaction on energy eigenvalues. In this step, we analyze the behaviors of their quartic energy eigenvalue polynomials in three sections and accurately compare all achieved physical-admissible roots one by one. This comparison surprisingly shows that the NC and NCP effects on the other hand, and the assumed harmonic energy-dependent interaction on the other hand, have almost the same order of perturbation effects for limited amounts of the magnetic field in a system of DKP bosons. Furthermore, through some calculations within this paper, we came up with a very crucial point about the NU method which was mistakenly being used in many papers by several researchers and improved it to be used safely.

In this paper, the spin-one Duffin–Kemmer–Petiau equation in (1 + 3) dimensions with a modified Kratzer potential is considered in the non-commutative space framework. The energy eigenvalue equation and the corresponding eigenfunctions are derived analytically. Furthermore, the energy shift due to the space non-commutativity effect is also obtained using the perturbation theory. In particular, it is shown that the degeneracy of the initial spectral line is broken, where the space non-commutativity plays the role of a magnetic field. This behavior is very similar to the Zeeman effect.

We investigate the generalized form of Duffin–Kemmer–Petiau (DKP) equation in the presence of both a position-dependent electrical field and curved spacetime for the 2-dimensional anti-de Sitter spacetime. Moreover, we derive both the asymptotic wave function and construct energy quantization with the help of the properties of gamma function. All thermodynamic quantities of the system have been calculated with the help of the Euler–MacLaurin formula in the final state.

In this paper, we investigate the approximate analytical solutions of the relativistic Duffin–Kemmer–Petiau equation in the presence of a Mie-Type potential in noncommutative space by using the Nikiforov–Uvarov method. We determine the energy eigenvalues and eigenfunctions of the DKP equation. Furthermore, energy shift due to noncommutativity space–time is obtained via the perturbation theory. We observe that this feature is comparable to the Zeeman effect and the degeneracy of the classical spectral line is fractured in the transition from commutative to noncommutative space by the splitting of the states.

In this paper, we study the covariant Duffin-Kemmer-Petiau (DKP) equation in the cosmic-string space-time and consider the interaction of a DKP field with the gravitational field produced by topological defects in order to examine the influence of topology on this system. We solve the spin-zero DKP oscillator in the presence of the Cornell interaction with a rotating coordinate system in an exact analytical manner for nodeless and one-node states by proposing a proper ansatz solution.

In this paper, a relativistic behavior of spin-zero bosons is studied in a chiral cosmic string space–time. The Duffin–Kemmer–Petiau (DKP) equation and DKP oscillator are written in this curved space–time and are solved by using an appropriate ansatz and the Nikiforov–Uvarov method, respectively. The influences of the topology of this space–time on the DKP spinor and energy levels and current density are also discussed in detail.

We study analytically the two-dimensional deformed bosonic oscillator equation for charged particles (both spin 0 and spin 1 particles) subject to the effect of an uniform magnetic field. We consider the presence of a minimal uncertainty in momentum caused by the anti-de Sitter model and we use the Nikiforov–Uvarov (NU) method to solve the system. The exact energy eigenvalues and the corresponding wave functions are analytically obtained for both Klein–Gordon and scalar Duffin–Kemmer–Petiau (DKP) cases and we find that the deformed spectrum remains discrete even for large values of the principal quantum number. For spin 1 DKP case, we deduce the behavior of the DKP equation and write the nonrelativistic energies and we show that the space deformation adds a new spin-orbit interaction proportional to its parameter. Finally, we study the thermodynamic properties of the system and here we find that the effects of the deformation on the statistical properties are important only in the high-temperature regime.

In this paper, we study the Duffin–Kemmer–Petiau (DKP) equation in the presence of a smooth barrier in dimensions space–time (1+1) dimensions. The eigenfunctions are determined in terms of the confluent hypergeometric function $M(\alpha ;\beta ;y)$. The transmission and reflection coefficients are calculated, special cases as a rectangular barrier and step potential are analyzed. A numerical study is presented for the transmission and reflection coefficients graphs for some values of the parameters $(V_0,E)$ are plotted.

In this paper, we solve the Duffin–Kemmer–Petiau (DKP) equation in the presence of hyperbolic tangent potential for spin-one particles. By partitioning the spin-one spinor, we show that the DKP equation is equivalent to the Klein–Gordon equation formalism. The scattering solutions are derived in terms of hypergeometric functions. The reflection $R$ and transmission $T$ coefficients are calculated in terms of the Gamma functions. The results show the presence of the superradiance phenomenon when $R$ for a specific region in the potential becomes greater than one.

This paper explores the topic of relativistic particles with zero spins from a unique perspective. Our approach is derived from the Dunkl derivative, which we used to investigate this issue. By examining the ($1+1$)-dimensional DKP equation, we obtain eigenfunctions. Additionally, we replace the standard partial derivative with the Dunkl derivative and solve the relativistic particle problem in a box using the new formalism. We then determine the energy spectrum for this scenario. Following this, we investigate the scattering of the potential step problem and the Ramsauer–Townsend effect separately. Finally, we calculate the coefficients of transmission and reflection.

The Duffin–Kemmer–Petiau (DKP) particle with spin 0 interacts with the Aharonov–Bohm (AB) magnetic vector potential and scalar Coulomb-type potential in the cosmic string space–times under the framework of rainbow gravity (RG). By using Bethe–Ansatz method, we obtain the energy eigenvalue and approximate solution to the wave function of the DKP particle with spin 0. We select two sets of rainbow functions and analyze their influence on the energy eigenvalue and wave functions. We find that the energy eigenvalue is determined by the parameters of the rainbow function. It further shows that the rainbow function affects the properties of the space–time where the DKP particle located, and also affects the distribution probability of DKP particles in the space.

In this paper, we solve the Duffin–Kemmer–Petiau equation in the presence of the cusp potential for spin-one particles. We derived the scattering solutions and calculated the bound states in terms of the Whittaker functions. We show that transmission resonances are present, as well as the particle–anti-particle bound states.

Doubly Special Relativity (DSR) is a promising candidate for understanding quantum gravity, by introducing two fundamental invariant scales — the speed of light and the Planck energy. Recently, another such theory has been proposed by Magueijo and Smolin (MS), and it can be extended to the whole class of DSRs. These models have structural similarity with different realizations of $\kappa$-Poincaré algebras. Given the significant implications of this theory, we explore the three-dimensional Duffin–Kemmer–Petiau (DKP) oscillator within this framework. By using the vector spherical harmonics technique in the momentum space, the three-dimensional DKP oscillator equation for spins 1 and 0 is reformulated from the viewpoint of the generalized algebra of the MS model. In order to recognize the influence of this reformulation, the energy eigenvalues contain an additional correction which depends on the deformation parameter, and eigenfunctions are determined in terms of the associated Laguerre polynomials.

The scattering of spin-1 bosons in a nonminimal vector double-step potential is described in terms of eigenstates of the helicity operator and it is shown that the transmission coefficient is insensitive to the choice of the polarization of the incident beam. Poles of the transmission amplitude reveal the existence of a two-fold degenerate spectrum. The results are interpreted in terms of solutions of two coupled effective Schrödinger equations for a finite square well with additional δ-functions situated at the borders.

We have investigated the Duffin–Kemmer–Petiau (DKP) equation, with equally vector and scalar potentials for the general deformed Morse potential, then we obtained creation and annihilation operators and showed that these operators satisfied the commutation relation of the $\mathrm{\text{SU}}(1,1)$group. The Casimir operator defined for Laguerre polynomials.