Related papers: The Spinless Relativistic Kink-Like Problem
We provide sufficient conditions to have at least one $N$-particle bound state below the essential spectrum of a large class of $N$-particle discrete Schr\"odinger operators $H(K),$ $K\in \mathbb{T}^d,$ $d\ge1,$ associated to the…
Correlation functions and form factors in vertex models or spin chains are known to satisfy certain difference equations called the quantum Knizhnik-Zamolodchikov equations. We find similar difference equations for the case of semi-infinite…
We consider a quasi-linear parabolic equation with nonlinear dynamic boundary conditions occurring as a natural generalization of the semilinear reaction-diffusion equation with dynamic boundary conditions. The corresponding class of…
We study spectral and scattering properties of a spinless quantum particle confined to an infinite planar layer with hard walls containing a finite number of point perturbations. A solvable character of the model follows from the explicit…
Semiclassical approximation to the Wheeler-DeWitt equation which corresponds to gravity with a minimally coupled scalar field has been performed. To the leading order, vacuum Einstein's equation along with the functional Schrodinger…
Bound q\bar q -systems are considered in the framework of three different versions of the 3-dimensional reduction of the Bethe-Salpeter equation, all having the correct one-body limit when one of the constituent quark masses tends to…
Recently, scattering of a Klein-Gordon particle in the presence of mixed scalar-vector generalized symmetric Woods-Saxon potential was investigated for the spin symmetric and the pseudo-spin symmetric limits in one spatial dimension. In…
We show that in classical mechanics, as well as in nonrelativistic quantum mechanics the equation of the relative motion for a two-body bound system at rest can be replaced by individual dynamical equations of the same kind as the first…
The explicit semiclassical treatment of logarithmic perturbation theory for the bound-state problem within the framework of the radial Klein-Gordon equation with attractive real-analytic screened Coulomb potentials, contained time-component…
We approximate the two-body spinless Salpeter equation with the one which is valid in heavy quarks limit. We consider the resulting semi-relativistic equation in a time-dependent formulation. We use the Lewis- Riesenfeld dynamical invariant…
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 consider the cubic nonlinear Schr\"{o}dinger equation in two space dimensions with an attractive potential. We study the asymptotic stability of the nonlinear bound states, i.e. periodic in time localized in space solutions. Our result…
The bound-state problem for an uncharged massive scalar particle in the field of a naked Reissner-Nordstr\"om singularity is approached by means of the quasiclassical Bohr-Sommerfeld quantization. An approximate analytical expression for…
The Kepler problem concerns a point particle in an attractive inverse square force. After a brief review of the classical and quantum versions of this problem, focused on their hidden $\text{SU}(2) \times \text{SU}(2)$ symmetry, we discuss…
In this paper we present an elementary derivation of the semi-classical spectrum of neutral particles in a field theory with kink excitations. In the non-integrable cases, we show that each vacuum state cannot generically support more than…
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…
Firstly, a systematic procedure is derived for obtaining three-dimensional bound-state equations from four-dimensional ones. Unlike ``quasi-potential approaches'' this procedure does not involve the use of delta-function constraints on the…
We analyze the behavior of the energy spectrum of the Klein-Gordon equation in the presence of a truncated hyperbolic tangent potential. From our analysis we obtain that, for some values of the potential there is embedding of the bound…
We consider a class of Cahn-Hilliard equation with kinetic rate dependent dynamic boundary conditions that describe possible short-range interactions between the binary mixture and the solid boundary. In the presence of surface diffusion on…
We propose a new analytical method to solve for the nonexactly solvable Schrodinger equation. Successfully, it is applied to a class of spiked harmonic oscillators and truncated Coulomb potentials. The utility of this method could be…