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For a class of long-range potentials, including ultra-strong perturbations of the attractive Coulomb potential in dimension $d\geq3$, we introduce a stationary scattering theory for Schr\"odinger operators which is regular at zero energy.…
The exact two-particle energy eigenstates in an asymmetric rectangular box with periodic boundary conditions in all three directions are studied. Their relation with the elastic scattering phases of the two particles in the continuum are…
The short-distance production of multi-particle states in high-energy nuclear reactions provides a unique way to study the low-energy properties of few-body systems. In particular, the production amplitude of multi-neutron systems is…
We discuss the three-body properties of identical bosons exhibiting large scattering length in two spatial dimensions. Within an effective field theory for resonant interactions, we calculate the leading non-universal corrections from the…
We study scatterings of bosonic massive closed string states at arbitrary mass levels from D-brane. We discover that all the scattering amplitudes can be expressed in terms of the generalized hypergeometric function with special arguments,…
Lorentz invariance, unitarity, and causality enforce powerful constraints on the theory space of physical scattering amplitudes. However, virtually all efforts in this direction have centered on the very simplest case of four-point…
We study the localization of eigenfunctions produced by a point scatterer on a thin rectangle. We find an explicit set of eigenfunctions localized to part of the rectangle by showing that the one-dimensional Schr\"odinger operator with a…
High-energy limit of zero-norm states (HZNS) in the old covariant first quantized (OCFQ) spectrum of the 26D open bosonic string, together with the assumption of a smooth behavior of string theory in this limit, are used to derive…
The momentum space zero-range model is used to investigate universal properties of three interacting particles confined to two dimensions. The pertinent equations are first formulated for a system of two identical and one distinct particle…
We study the cubic-quintic NLS in three space dimensions. It is known that scattering holds for solutions with mass-energy in a region corresponding to positive virial, the boundary of which is delineated both by ground state solitons and…
We obtain the exact energy spectrum of nonuniform mass particles for a collection of Hamiltonians in a three-dimensional approach to a quantum dot. By considering a set of generalized Schr\"odinger equations with different orderings between…
In addition to the conventional renormalized--coupling--constant picture, point interactions in dimension two and three are shown to model within a suitable energy range scattering on localized potentials, both attractive and repulsive.
The method of zero-range potentials is generalized to account for the molecular electron excitation process. It is made by a matrix formulation in which a state vector components are associated with a scattering channel. The multi-center…
The energy spectrum of a 3-level atomic system in the $\Xi$-configuration is studied. This configuration presents a triple point independently of the number of atoms, which remains in the thermo- dynamic limit. This means that in a vicinity…
Orthogonality of eigenstates of different energies and its implications in potential scattering are unlabeled. Scalar products of scattering states of different energies are found to have finite non-orthogonal terms in potentials of finite…
In this work we report on recent progress in the calculation of open superstring scattering amplitudes, at tree level, with more than four external massless states. We also report on the corresponding terms in the low energy effective…
Two different aspects of the description of three- and four-nucleon systems are addressed. The use of bound state like wave functions to describe scattering states in $N-d$ collisions at low energies and the effects of some of the widely…
We describe structure of the T-matrices, scattering matrices, and Green functions on unphysical energy sheets in multichannel scattering problems with binary channels and in the three-body problem. Based on the explicit representations…
We show that quantum fluctuations of electromagnetic fields induce an additional zero-point energy in solids, which scales with the volume. For insulators, the zero-point energy density is proportional to quantum fluctuation of electric…
We derive the asymptotic expansions of the wave function of three particles having equal mass with finite-range interactions and infinite or zero two-dimensional scattering length colliding at zero energy and zero orbital angular momentum,…