Related papers: The Spinless Relativistic Hellmann Problem
We demonstrate that the analytic solution for the set of energy eigenvalues of the semi-relativistic Coulomb problem reported by B. and L. Durand is in clear conflict with an upper bound on the ground-state energy level derived by some…
Using relativistic tensor-bispinorial equations proposed in hep-th/0412213 we solve the Kepler problem for a charged particle with arbitrary half-integer spin interacting with the Coulomb potential.
We study the spectrum of the spinless-Salpeter Hamiltonian H = \beta \sqrt{m^2 + p^2} + V(r), where V(r) is an attractive central potential in three dimensions. If V(r) is a convex transformation of the Coulomb potential -1/r and a concave…
We obtain analytical solutions of the two-body spinless Salpeter (SS) equation with Yukawa potential within the conventional approximation scheme to the centrifugal term for any -state. The semi-relativistic bound state energy spectra and…
The Hamiltonian of the spinless relativistic Coulomb problem combines the standard Coulomb interaction potential with the square-root operator of relativistic kinematics. This Hamiltonian is known to be bounded from below up to some…
In this paper, we present the Dirac equation for the Mobius-square-Yukawa potentials including the tensor interaction term within the framework of pseudospin and spin symmetry limit with arbitrary spin-orbit quantum number . We obtained the…
Using the auxiliary field method, a generic upper bound is obtained for the spinless Salpeter equation with two different masses. Analytical results are presented for the cases of the Coulomb and linear potentials when a mass is vanishing.
We examine the bound state solutions of the Dirac equation under the spin and pseudospin symmetries for a new suggested combined potential, Hulten plus a class of Yukawa potential including a Coulomb-like tensor interaction. An improved…
We investigate the relativistic effects of a moving particle in the field of a pseudo-harmonic oscillatory ring-shaped potential under the spin and pseudo-spin symmetric Dirac wave equation. We obtain the bound state energy eigenvalue…
It has been unknown in kinetic theory whether the linearized Boltzmann or Landau equation with soft potentials admits a spectral gap in the spatially inhomogeneous setting. Most of existing works indicate a negative answer because the…
We have used different methods to obtain the bound states of a Hamiltonian of a relativistic two scalar particle system in a local potential. The potentials we are interested in are binding and confining potentials, that are associated with…
We study the removability of a singular set in the boundary of Neumann problem for elliptic equations with variable exponent. We consider the case where the singular set is compact, and give sufficient conditions for removability of this…
In this paper, we construct an analytical solution of the one-dimensional spinless Salpeter equation with a Coulomb potential supplemented by a hard core interaction, which keeps the particle in the x positive region.
Several techniques for deriving semianalytical bounds on the energy eigenvalues of the spinless Salpeter equation and for estimating the quality of the corresponding approximate eigenstates are reviewed.
Several results related to flat Friedmann-Lema\^{\i}tre-Robertson-Walker models in the conformal (Einstein) frame of scalar-tensor gravity theories are extended. Scalar fields with arbitrary (positive) potentials and arbitrary coupling…
A covariant hamiltonian formalism for the dynamics of compact spinning bodies in curved space-time in the test-particle limit is described. The construction allows a large class of hamiltonians accounting for specific properties and…
Analytic and approximate solutions for the energy eigenvalues generated by a confined softcore Coulomb potentials of the form a/(r+\beta) in d>1 dimensions are constructed. The confinement is effected by linear and harmonic-oscillator…
In quantum theory, bound states are described by eigenvalue equations, which usually cannot be solved exactly. However, some simple general theorems allow to derive rigorous statements about the corresponding solutions, that is, energy…
The Dirac Equation is solved approximately for relativistic generalized Woods-Saxon potential including Coulomb-like tensor potential in exact pseudospin and spin symmetry limits. The bound states energy eigenvalues are found by using…
We analyze the fully relativistic, field-theoretical treatment of the scalar Coulomb problem. We work in a truncated Hilbert-Fock space containing the two-constituent states and the two-constituent-and-one-massless-exchange-particle states.…