134,689 research outputs found
An exact solution to the Dirac equation for a time dependent Hamiltonian in 1-1D space-time
We find an exact solution to the Dirac equation in 1-1 dimensional space-time
in the presence of a time-dependent potential which consists of a combination
of electric, scalar, and pseudoscalar terms.Comment: Five page
On the Dirac equation with PT-symmetric potentials in the presence of position-dependent mass
The relativistic problem of fermions subject to a PT-symmetric potential in
the presence of position-dependent mass is reinvestigated. The influence of the
PT-symmetric potential in the continuity equation and in the orthonormalization
condition are analyzed. In addition, a misconception diffused in the literature
on the interaction of neutral fermions is clarified.Comment: 8 page
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.
Quasi-exactly-solvable confining solutions for spin-1 and spin-0 bosons in (1+1)-dimensions with a scalar linear potential
We point out a misleading treatment in the recent literature regarding
confining solutions for a scalar potential in the context of the
Duffin-Kemmer-Petiau theory. We further present the proper bound-state
solutions in terms of the generalized Laguerre polynomials and show that the
eigenvalues and eigenfunctions depend on the solutions of algebraic equations
involving the potential parameter and the quantum number.Comment: 8 pages, 1 figur
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
Quantitative Isoperimetric Inequalities on the Real Line
In a recent paper A. Cianchi, N. Fusco, F. Maggi, and A. Pratelli have shown
that, in the Gauss space, a set of given measure and almost minimal Gauss
boundary measure is necessarily close to be a half-space. Using only geometric
tools, we extend their result to all symmetric log-concave measures \mu on the
real line. We give sharp quantitative isoperimetric inequalities and prove that
among sets of given measure and given asymmetry (distance to half line, i.e.
distance to sets of minimal perimeter), the intervals or complements of
intervals have minimal perimeter.Comment: 14 pages, 3 figure
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