Related papers: Wave kernels with magnetic field on the hyperbolic…
This paper deals with exact formulas for the resolvent kernels and exact solutions of time dependent Schr\"odinger equations under a uniform magnetic field on the hyperbolic half plane $\H$, and under a diatomic molecular Morse potential on…
In this note we give an explicit formula for the wave equation associated to the Schrodinger operator with a Liouville Potential with applications to the telegraph equation as well as the wave equation on the hyperbolic plane
In this paper we give an integral representation for the resolvent kernels with uniform magnetic field on the hyperbolic plane, as applications of our results we solve explicitly two times dependent Schr\"odinger equations with uniform…
The Schwartz kernel of the spectral density for the Schr\"{o}dinger operator with magnetic field in the $n-$dimensional complex ball is given. As applications, we compute the heat, resolvent and the wave kernels. Moreover, the resolvent and…
We consider the zigzag half-nanotubes (tight-binding approximation) in a uniform magnetic field which is described by the magnetic Schr\"odinger operator with a periodic potential plus a finitely supported perturbation. We describe all…
We prove existence results and lower bounds for the resonances of Schr\"odinger operators associated to smooth, compactly support potentials on hyperbolic space. The results are derived from a combination of heat and wave trace expansions…
We prove that for the mass critical nonlinear Schrodinger equations, the wave operators and their inverse are related explicitly in terms of the Fourier transform. We discuss some consequences of this property. In the one-dimensional case,…
We provide a simple sufficient condition in an abstract framework to deduce the existence and completeness of wave operators (resp. modified wave operators) on Sobolev spaces from the existence and completeness of the usual wave operators…
In this work we give explicit formulas for the Schwartz integral kernels of some multipliers of the Schr\"odinger operator with inverse square potential on $\R^\ast_+$. By using the integral transforms connecting these multipliers we obtain…
One-dimensional Schr\"odinger operators with singular perturbed magnetic and electric potentials are considered. We study the strong resolvent convergence of two families of the operators with potentials shrinking to a point. Localized…
The aim of the paper is to derive spectral estimates on the eigenvalue moments of the magnetic Schroedinger operators defined on the two-dimensional disk with a radially symmetric magnetic field and radially symmetric electric potential.
In this note we give explicit solutions to the wave equation associated to the Schr\"odinger operator with three-inverse square potential on $R_+^3$
We present here a systematic and unified treatment to connect the Schrodinger equation corresponding to generalized Morse and Poschl-Teller potentials. We then show that the wave functions and generalized potentials are linked through the…
We construct time-dependent wave operators for Schr\"{o}dinger equations with long-range potentials on a manifold $M$ with asymptotically conic structure. We use the two space scattering theory formalism, and a reference operator on a space…
The Schr\"odinger equation is solved for the wave function of an electron moving in a superposition of external constant and uniform electric and magnetic fields at an arbitrary angle between the field directions. The changing of the…
We investigate the kernels of the transformation operators for one-dimensional Schroedinger operators with potentials, which are asymptotically close to Bohr almost periodic infinite-gap potentials.
We prove existence of modified wave operators for one-dimensional Schr\"odinger equations with potential in $L^p(\reals)$, $p<2$. If in addition the potential is conditionally integrable, then the usual M\"oller wave operators exist. We…
The quantum behavior of electrons in bilayer graphene with applied magnetic fields is addressed. By using second-order supersymmetric quantum mechanics the problem is transformed into two intertwined one dimensional stationary Schr\"odinger…
This paper deals with the approximation of a magnetic Schr\"odinger operator with a singular $\delta$-potential that is formally given by $(i \nabla + A)^2 + Q + \alpha \delta_\Sigma$ by Schr\"odinger operators with regular potentials in…
This work deals with Schr\"odinger equations with quadratic and sub-quadratic Hamiltonians perturbed by a potential. In particular we shall focus on bounded, but not necessarily smooth perturbations. We shall give a representation of such…