Related papers: Faddeev eigenfunctions for two-dimensional Schrodi…
A novel approach to solve the Faddeev equation for three-body scattering at arbitrary energies is proposed. This approach disentangles the complicated singularity structure of the free three-nucleon propagator leading to the moving and…
We study the presence of symmetry transformations in the Faddeev-Jackiw approach for constrained systems. Our analysis is based in the case of a particle submitted to a particular potential which depends on an arbitrary function. The method…
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…
We prove conditions on potentials which imply that the sum of the negative eigenvalues of the Schroeodinger operator is finite. We use a method for bounding eigenvalues based on estimates of the Hilbert-Schmidt norm of semigroup differences…
The Schr\"{o}dinger equation in $D$-dimensions for the Manning-Rosen potential with the centrifugal term is solved approximately to obtain bound states eigensolutions (eigenvalues and eigenfunctions). The Nikiforov-Uvarov(NU) method is used…
Faddeev equations in configuration space and integral form for three-atom scattering processes are formulated allowing for additive and nonadditive forces. The explicit partial wave decomposition is displayed. This formulation appears to be…
For Schr\"odinger operators $H_V=-\Delta_g+V$ with critically singular potentials $V$ on compact manifolds, we prove sharp estimates for the restriction of eigenfunctions to submanifolds. Our method refines the perturbative argument by…
We give a sharp estimate of the number of zeros of analytic functions in the unit disc belonging to analytic quasianalytic Carleman--Gevrey classes. As an application, we estimate the number of the eigenvalues for discrete Schr\"odinger…
Using the inverse scattering method, we construct global solutions to the Novikov-Veselov equation for real-valued decaying initial data q with the property that the associated Schrodinger operator with potential q is nonnegative. Such…
We prove that if a solution of the discrete time-dependent Schr\"odinger equation with bounded real potential decays fast at two distinct times then the solution is trivial. For the free Shr\"odinger operator and for operators with…
We give three formulas for meromorphic eigenfunctions (scattering states) of Sutherland's integrable N-body Schroedinger operators and their generalizations. The first is an explicit computation of the Etingof-Kirillov traces of…
The representations of the kernels of the transmutation operator and of its inverse relating the one-dimensional Schr\"odinger operator with the second derivative are obtained in terms of the eigenfunctions of a corresponding…
The Schrodinger equations which are exactly solvable in terms of associated special functions are directly related to some self-adjoint operators defined in the theory of hypergeometric type equations. The fundamental formulae occurring in…
An explicit formula for the wave operators associated with Schroedinger operators on the discrete half-line is deduced from their stationary expressions. The formula enables us to understand the wave operators as one dimensional…
We prove that the singularities of a potential in the two and three dimensional Schr\"odinger equation are the same as the singularities of the Born approximation (Diffraction Tomography), obtained from backscattering inverse data, with an…
Momentum space three-body Faddeev-like equations are used to calculate elastic, transfer and charge exchange reactions resulting from the scattering of deuterons on 12C and 16O or protons on 13C and 17O; 12C and 16O are treated as inert…
We study the asymptotic behavior, in a ``semi-classical limit'', of the first eigenvalues (i.e. the groundstate energies) of a class of Schr\"{o}dinger operators with magnetic fields and the relationship of this behavior with compactness in…
An exactly solvable position-dependent mass Schr\"odinger equation in two dimensions, depicting a particle moving in a semi-infinite layer, is re-examined in the light of recent theories describing superintegrable two-dimensional systems…
We derive a pseudopotential in two dimensions (2D) with the presence of a 2D Rashba spin-orbit-coupling (SOC), following the same spirit of frame transformation in {[}Phys. Rev. A 95, 020702(R) (2017){]}. The frame transformation correctly…
We describe two-dimensional potential Schrodinger and Dirac operators which are finite-gap at one energy level and have singular spectral curves. It appears that the singularities can be rather complicated. Such Dirac operators appear as…