Related papers: Effective-Mass Klein-Gordon-Yukawa Problem for Bou…
The interface problem describing the scattering of time-harmonic electromagnetic waves by a dielectric body is often formulated as a pair of coupled boundary integral equations for the electric and magnetic current densities on the…
For a damped wave (or Klein-Gordon) equation on a bounded domain, with a focusing power-like nonlinearity satisfying some growth conditions, we prove that a global solution is bounded in the energy space, uniformly in time. Our result…
We study a new approach to generally covariant quantum mechanics applied in the case of an FLRW cosmological background. For positive spatial curvature we find a discrete series of solutions of the Klein-Gordon equation that can reasonably…
We establish the scattering of solutions to the focusing mass supercritical nonlinear Schr\"odinger equation with a repulsive Dirac delta potential \[ i\partial_{t}u+\partial^{2}_{x}u+\gamma\delta(x)u+|u|^{p-1}u=0, \quad (t,x)\in {\mathbb…
Three-boson Efimov physics is well known in the bound-state regime, but far less in the three-particle continuum at negative two-particle scattering length where Efimov states evolve into resonances. They are studied solving rigorous…
The most important parameters in the study of low-energy scattering are the s-wave and p-wave scattering lengths and the s-wave effective range. We solve the scattering problem and find two useful formulas for the scattering length and the…
This paper is concerned with strong blow-up instability (Definition 1.3) for standing wave solutions to the system of the quadratic nonlinear Klein-Gordon equations. In the single case, namely the nonlinear Klein-Gordon equation with power…
Effective mass Schrodinger equation is solved exactly for a given potential. Nikiforov-Uvarov method is used to obtain energy eigenvalues and the corresponding wave functions. A free parameter is used in the transformation of the wave…
The Schr\"odinger-like equation written in terms of the displacement operator is solved analytically for a inverse square plus Coulomb-like potential. Starting from the new Hamiltonian, the effects of the spatially dependent mass on the…
A detailed consideration of the Klein-Gordon equation in relativistic quantum mechanics is presented in order to offer more clarity than many standard approaches. The equation is frequently employed in the research literature, even though…
In this paper, the bound state solution of the modified Klein-Fock-Gordon equation is obtained for the Hulth\'en plus ring-shaped lake potential by using the developed scheme to overcome the centrifugal part. The energy eigenvalues and…
We apply renormalisation-group methods to two-body scattering by a combination of known long-range and unknown short-range potentials. We impose a cut-off in the basis of distorted waves of the long-range potential and identify possible…
In this work, we obtained analytical bound state solution of the Schr\"odinger equation with Manning Rosen plus exponential Yukawa Potential using parametric Nikiforov-Uvarov method (NU). We obtained the normalized wave function in terms of…
Scattering in central attractive potentials is investigated systematically, in the limit of strong interaction, when large-angles scattering dominates. In particular, three important model interactions (Lennard-Jones, Yukawa, and…
The phenomenon of wave tails has attracted much attention over the years from both physicists and mathematicians. However, our understanding of this fascinating phenomenon is not complete yet. In particular, most former studies of the tail…
An approximation-free, numerically efficient algorithm is presented for the Hamiltonian eigen-states of the Stark-Hydrogen problem describing a quantum particle exposed to the central Coulomb force and a homogeneous external field. As an…
In this study, we discuss some general critical properties of bound states with one-boson-exchange potential. For simplicity, we first take a system with two identical scalar particles as an example. The interaction between these two scalar…
The Klein-Gordon equation in the presence of a spatially one-dimensional Hulth\'en potential is solved exactly and the scattering solutions are obtained in terms of hypergeometric functions. The transmission coefficient is derived by the…
We consider a nonlinear system of two-dimensional Klein-Gordon equations with masses satisfying the resonance relation. We introduce a structural condition on the nonlinearities under which the solution exists globally in time and decays at…
This article constitutes the final and main part of a three-paper sequence, whose goal is to prove global well-posedness and scattering of the energy critical Maxwell-Klein-Gordon equation (MKG) on $\mathbb{R}^{1+4}$ for arbitrary finite…