Related papers: On the wave operators for the Friedrichs-Faddeev m…
Ideas and results of the generalized wave operator theory for dynamical and stationary cases are developed further and exact expressions for generalized scattering operators are obtained for wide classes of differential equations. New…
Electromagnetic waves and fluids have locally conserved mechanical properties associated with them and we may expect these to exist for matter waves. We present a semiclassical description of the continuity equations relating to these…
We construct a time-dependent scattering theory for Schr\"odinger operators on a manifold $M$ with asymptotically conic structure. We use the two-space scattering theory formalism, and a reference operator on a space of the form $R\times…
Using waves to explore our environment is a widely used paradigm, ranging from seismology to radar technology, and from bio-medical imaging to precision measurements. In all of these fields, the central aim is to gather as much information…
A general representation formula for the scattering matrix of a scattering system consisting of two self-adjoint operators in terms of an abstract operator valued Titchmarsh-Weyl $m$-function is proved. This result is applied to scattering…
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…
An alternative description of quantum scattering processes rests on inhomogeneous terms amended to the Schroedinger equation. We detail the structure of sources that give rise to multipole scattering waves of definite angular momentum, and…
We discuss the structure of the two- and three-body T-matrices, scattering matrices, and resolvents continued to the unphysical energy sheets. Our conclusions arise due to the representations that have been found for analytically continued…
An integral representation of solutions of the wave equation as a superposition of other solutions of this equation is built. The solutions from a wide class can be used as building blocks for the representation. Considerations are based on…
Explicit formulas for the analytic extensions of the scattering matrix and the time delay of a quasi-one-dimensional discrete Schr\"odinger operator with a potential of finite support are derived. This includes a careful analysis of the…
A modeling methodology and matrix formalism is presented that permits analysis of arbitrarily complex interferometric waveguide systems, including polarization and backreflection effects. Considerable improvement results from separation of…
We prove a structure formula for the wave operators in R^3 and their adjoints for a scaling-invariant class of scalar potentials V, under the assumption that zero is neither an eigenvalue, nor a resonance for -\Delta+V. The formula implies…
In this paper we present the connection between scattering amplitudes in momentum space and wave functions in coordinate space, generalizing previous work done for s-waves to any partial wave. The relationship to the wave function of the…
We introduce the Hamiltonian dynamics with the Hartree-Fock energy in new {\it wave-matrix} picture. Roughly speaking, the wave matrix is defined as the square root of the density matrix. The corresponding Hamiltonian equations are…
We develop direct and inverse scattering theory for Jacobi operators which are short range perturbations of quasi-periodic finite-gap operators. We show existence of transformation operators, investigate their properties, derive the…
We give a definition of scattering matrices based on the asymptotic behaviors of generalized eigenfunctions and show that these scattering matrices are equivalent to the ones defined by wave-operator approach in long-range $N$-body…
We present explicit formulas for the Faddeev eigenfunctions and related generalized scattering data for multipoint potentials in two and three dimensions. For single point potentials in 3D such formulas were obtained in an old unpublished…
We develop a scattering theory for time-periodic Hamiltonians on discrete graphs, including long-range potentials with zero average for the period, and show the existence and completeness of wave operators.
Flat-space physics is highly constrained by basic principles such as Lorentz invariance, locality, unitarity and causality. This is neatly seen in the structure of scattering amplitudes. For processes occurring in an expanding background we…
In this follow-up article to [Shadow poles in the alternative parametrization of R-matrix theory, Ducru (2020)], we establish new results on scattering matrix pole expansions for complex wavenumbers in R-matrix theory. In the past, two…