Comment on "Wave functions for a Duffin-Kemmer-Petiau particle in a time-dependent potential"

It is shown that the paper "Wave functions for a Duffin-Kemmer-Petiau particle in a time-dependent potential", by Merad and Bensaid [J. Math. Phys. 48, 073515 (2007)] is not correct in using inadvertently a non-Hermitian Hamiltonian in a formalism that does require Hermitian Hamiltonians.Comment: 2 page

Corroborating the equivalence between the Duffin-Kemmer-Petiau and the Klein-Gordon and Proca equations

It is shown that the Hamiltonian version of the Duffin-Kemmer-Petiau theory with electromagnetic coupling brings about a source term at the current. It is also shown that such a source term disappears from the scenario if one uses the correct physical form for the Duffin-Kemmer-Petiau field, regardless the choice for representing the Duffin-Kemmer-Petiau matrices. This result is used to fix the ambiguity in the electromagnetic coupling in the Duffin-Kemmer-Petiau theory. Moreover, some widespread misconceptions about the Hermiticity in the Duffin-Kemmer-Petiau theory are discussed.Comment: 13 pages, to appears in Phys. Rev.

On the bound-state spectrum of a nonrelativistic particle in the background of a short-ranged linear potential

The nonrelativistic problem of a particle immersed in a triangular potential well, set forth by N.A. Rao and B.A. Kagali, is revised. It is shown that these researchers misunderstood the full meaning of the potential and obtained a wrong quantization condition. By exploring the space inversion symmetry, this work presents the correct solution to this problem with potential applications in electronics in a simple and transparent way

Missing solution in a Cornell potential

Missing bound-state solutions for fermions in the background of a Cornell potential consisting of a mixed scalar-vector-pseudoscalar coupling is examined. Charge-conjugation operation, degeneracy and localization are discussed

Relativistic Effects of Mixed Vector-Scalar-Pseudoscalar Potentials for Fermions in 1+1 Dimensions

The problem of fermions in the presence of a pseudoscalar plus a mixing of vector and scalar potentials which have equal or opposite signs is investigated. We explore all the possible signs of the potentials and discuss their bound-state solutions for fermions and antifermions. The cases of mixed vector and scalar P\"{o}schl-Teller-like and pseudoscalar kink-like potentials, already analyzed in previous works, are obtained as particular cases

Unified Treatment of Mixed Vector-Scalar Screened Coulomb Potentials for Fermions

The problem of a fermion subject to a general mixing of vector and scalar screened Coulomb potentials in a two-dimensional world is analyzed and quantization conditions are found.Comment: 7 page

Enumeration of kk-Fibonacci Paths using Infinite Weighted Automata

In this paper, we introduce a new family of generalized colored Motzkin paths, where horizontal steps are colored by means of $F_{k,l}$ colors, where $F_{k,l}$ is the $l$th $k$-Fibonacci number. We study the enumeration of this family according to the length. For this, we use infinite weighted automata.Comment: arXiv admin note: substantial text overlap with arXiv:1310.244

Transmission coefficient and two-fold degenerate discrete spectrum of spin-1 bosons in a double-step potential

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 Schr\"{o}dinger equations for a finite square well with additional $\delta$-functions situated at the borders.Comment: arXiv admin note: substantial text overlap with arXiv:1203.119