Solution of Duffin–Kemmer–Petiau Equation for the Step Potential

Quantum Speed Limit for Relativistic Spin-0 and Spin-1 Bosons on Commutative and Noncommutative Planes

“…The algebra (2) has three different representations: a (onedimensional) trivial representation, a five-dimensional representation describing spin-0 bosons, and a ten-dimensional representation describing spin-1 bosons. As a Dirac-type relativistic quantum mechanical model, DKP equation with various potentials has been studied in the past years [4][5][6][7][8].…”

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.…”

Matrix Continued Fraction Solution to the Relativistic Spin-0 Feshbach–Villars Equations

“…They split the Klein-Gordon wave function into two components and for the components vector they arrived at a Schrödinger-like equation with first order in time derivative. Although the Feshbach-Villars formalism appear in some advanced quantum mechanics books [9,10,11,12,13,14,15], and they were utilized in gaining deeper insight into relativistic physics of Klein paradox pair production, [16,17,18,19,20,21,22,23], in exotic atoms [24,25,26], used in theoretical consideraions [27,28,29,31], study relativistic scattering [32,32] and optics [33] or demosntrate PT symmetry [34,35,36,37], they were hardly used as a computational tool. The equations look like ordinary coupled differential equations, but the components are coupled by the kinetic energy operator, which makes them very hard to solve.…”