DKP Equation with Smooth Potential and Position-Dependent Mass

Abstract

The Duffin-Kemmer-Petiau (DKP) equation for spin 0 and 1 with smooth potential and position dependent-mass is solved. The solution is given in terms of the Heun function. The step case for potential and mass are deduced as a limiting case. The boundary conditions are also discussed.

Duffin-Kemmer-Petiau equation in Robertson-Walker space-time

“…The β µ are the Minkowski DKP matrices and all their properties are listed in [24][25][26][27][28] In order to study the effects of gravity on the DKP quantum mechanics. We can use the tetrad formalism [35], which is based on the principle of equivalence, to obtain the generalized DKP equation in the curved spacetime [33,36] …”

“…In the literature, there is another relativistic equation other than that of Dirac and Klein-Gordon, namely, the Duffin-Kemmer-Petiau (DKP) equation [21][22][23][24][25][26][27][28] This latter describes the dynamics of the scalar and vectorial particles spin 0 and 1, respectively.…”

Effects Due to a Scalar Coupling on the Particle-Antiparticle Production in the Duffin-Kemmer-Petiau Theory

“…The form ∂ 1 + iA 1 in (8) suggests that the space component of the minimal vector potential can be gauged away by defining a new spinorψ…”

“…Just as in the case of a pure vector coupling [2], there is no reason to require that the spinor and its derivative are continuous across finite discontinuities of the potential, as naively advocated in [3,8]. A careful analysis reveals, though, that proper matching conditions follow from the differential equations obeyed by the spinor components, as they should be, avoiding in this manner to recur to the limit process of smooth potentials.…”

Approximate Complete Solutions of DKP Equation under a Vector Exponential Interaction via a Pekeris-Type Approximation

“…In addition, the DKP equation is richer in the investigation of interactions and is even closer to some experimental data in comparison with KG or Proca equations 15-20 . Moreover, besides cosmology and gravity, this equation has been tested in many branches of physics including particle and nuclear physics 21-25 . As usual, the most appealing case studies are Coulomb and quadratic terms 26-28 , and other ones including the woods-Saxon and Hulthen are investigated by different 2 ISRN High Energy Physics approaches as well [29][30][31][32] . Within the present work, we first review the DKP equation.…”