Related papers: Phase equivalent chains of Darboux transformations…
In this paper, we consider the existence and the asymptotic completeness of the wave operators for Schrodinger equations with time-dependent potentials which are short-range in space.
In quantum scattering theory, there exists a relationship between the difference in the scattering phase shifts at threshold and infinity and the number of bound states, which is established by the Levinson theorem. The presence of…
Shallow one-dimensional double well potentials appear in atomic and molecular physics and other fields. Unlike the "deep" wells of macroscopic quantum coherent systems, shallow double wells need not present low-lying two-level systems. We…
An ordinary differential operator of the fourth order with coefficients converging at infinity sufficiently rapidly to constant limits is considered. Scattering theory for this operator is developed in terms of special solutions of the…
Making use of the analytical properties of the $S$-matrix and a theorem of Mittag-Leffler, model independent non-relativistic expressions for cross sections in single channel elastic scattering, scattering phase shifts and survival…
An exact method for direct calculation of the Jost functions and Jost solutions for non-central potentials which couple partial waves of different angular momenta is presented. A combination of the variable-constant method with the complex…
A dressing of a nonspherical potential, which includes $n$ zero range potentials, is considered. The dressing technique is used to improve ZRP model. Concepts of the partial waves and partial phases for non-spherical potential are used in…
In this paper, we study the scattering theory for the cubic inhomogeneous Schr\"odinger equations with inverse square potential $iu_t+\Delta u-\frac{a}{|x|^2}u=\lambda |x|^{-b}|u|^2u$ with $a>-\frac14$ and $0<b<1$ in dimension three. In the…
We develop a complete stationary scattering theory for Schr\"odinger operators on $\mathbb R^d$, $d\ge 2$, with $C^2$ long-range potentials. This extends former results in the literature, in particular [Is1, Is2, II, GY], which all require…
We consider semiclassical Schr\"odinger operators on the real line of the form $$H(\hbar)=-\hbar^2 \frac{d^2}{dx^2}+V(\cdot;\hbar)$$ with $\hbar>0$ small. The potential $V$ is assumed to be smooth, positive and exponentially decaying…
We construct a complete conformal scattering theory for finite energy Maxwell potentials on a class of curved, asymptotically flat spacetimes with prescribed smoothness of null infinity and a non-zero ADM mass. In order to define the full…
In this work, the phase function method (PFM) is employed for the first time to explicitly construct scattering wavefunctions for the $\alpha\alpha$ system using a single-term Morse potential. Unlike earlier PFM-based studies that primarily…
We study the scattering problem, the Sturm-Liouville problem and the spectral problem with periodic or skew-periodic boundary conditions for the one-dimensional Schr\"odinger equation with an $n$-cell (finite periodic) potential. We give…
We analyze how a short distance boundary condition for the Schrodinger equation must change as a function of the boundary radius by imposing the physical requirement of phase shift independence on the boundary condition. The resulting…
Similarity symmetries of the factorization chains for one-dimensional differential and finite-difference Schr\"odinger equations are discussed. Properties of the potentials defined by self-similar reductions of these chains are reviewed. In…
We offer a consistent dynamical formulation of stationary scattering in two and three dimensions that is based on a suitable multidimensional generalization of the transfer matrix. This is a linear operator acting in an infinite-dimensional…
Using the pruned-enriched Rosenbluth Monte Carlo algorithm, the scattering functions of semiflexible macromolecules in dilute solution under good solvent conditions are estimated both in $d=2$ and $d=3$ dimensions, considering also the…
This work deals with the functional model for a class of extensions of symmetric operators and its applications to the theory of wave scattering. In terms of Boris Pavlov's spectral form of this model, we find explicit formulae for the…
A semianalytical approach is developed to calculate the effective pair potential of rigid arbitrarily shaped macroions with a nonvanishing particle volume, valid within linear screening theory and the mean-field approximation. The essential…
Scattering of charged particles is ubiquitous in nuclear physics. We calculate the proton-proton $s$-wave phase shift at low energy relevant to solar physics. The phase shift is calculated from the ratio of the regular and irregular…