Related papers: Exact Solution of a N-body Problem in One Dimensio…
A general definition of energy is given, via the N\"other theorem, for the N-body problem in (1+1) dimensional gravity. Within a first-order Lagrangian framework, the density of energy of a solution relative to a background is identified…
We announce the existence and uniqueness theorem for the scattering problem of three one-dimensional quantum particles interacting by repulsive finite pair potentials
The one-dimensional scattering of a two body interacting system by an infinite wall is studied in a quantum-mechanical framework. This problem contains some of the dynamical features present in the collision of atomic, molecular and nuclear…
Systems that involve N identical interacting particles under quantum confinement appear throughout many areas of physics, including chemical, condensed matter, and atomic physics. In this paper, we present the methods of dimensional…
It is shown that in the case of the one-particle one-dimensional scattering problem for a given time-independent potential, for each state of the whole quantum ensemble of identically prepared particles, there is an unique pair of…
A solution of the scattering problem is obtained for the Schr\"odinger equation with the potential of induced dipole interaction, which decreases as the inverse square of the distance. Such a potential arises in the collision of an incident…
We report on a study of a finite system of classical confined particles in two-dimensions in the presence of a uniform magnetic field and interacting via a two-body repulsive potential. We develop a simple analytical method of analysis to…
We consider a one-dimensional matter-wave bright soliton, corresponding to the ground bound state of N particles of mass m having a binary attractive delta potential interaction on the open line. For a full N-body quantum treatment, we…
Within a scalar model theory of gravity, where the interaction between particles is given by the half-retarded + half-advanced solution of the scalar wave equation, we consider an N-body problem: we investigate configurations of N particles…
An ansatz describing in terms of formal asymptotic decompositions a leading term of asymptotics of the $n$ three-dimensional like-charged quantum particles scattering problem solution is suggested. The description of the solution in those…
We consider the multidimensional (nonrelativistic) Newton equation in a static electromagnetic field $$\ddot x = F(x,\dot x), F(x,\dot x)=-\nabla V(x)+B(x)\dot x, \dot x={dx\over dt}, x\in C^2(\R,\R^n),\eqno{(*)}$$ where $V \in…
The quantum $N$-body problem is studied in the context of nonrelativistic quantum mechanics with a one-dimensional deformed Heisenberg algebra of the form $[\hat x,\hat p]=i(1+\beta \hat p^2)$, leading to the existence of a minimal…
The nucleon-nucleon (NN) t-matrix is calculated directly as function of two vector momenta for different realistic NN potentials. To facilitate this a formalism is developed for solving the two-nucleon Lippmann-Schwinger equation in…
The goal of this paper is to construct an effective model for studying the asymptotic solution of the scattering problem of three one-dimensional quantum particles with finite (short-range) attractive pair potentials. The asymptotic nature…
The mathematically exact solution of a one-dimensional (1D) quantum N-identical-boson system with zero-range pair interaction has been well known. We find that this solution is non-physical, since there exists a paradox of its energy…
The discrete energy-eigenvalues of two nucleons interacting with a finite-range nuclear force and confined to a harmonic potential are used to numerically reconstruct the free-space scattering phase shifts. The extracted phase shifts are…
We employ generalized Euler coordinates for the $n$ body system in $d \geq n-1$ dimensional space, which consists of the centre-of-mass vector, relative (mutual), mass-independent distances $r_{ij}$ and angles as remaining coordinates. We…
We present an exact solution to the one-dimensional (1-D) scattering-from-a-barrier problem for an incident neutron described by a wave packet. As an aid to presenting our approach, we spend some time on a basic review of how wave packets…
When we use variational methods to study the Newtonian $N$-body problem, the main problem is how to avoid collisions. C.Marchal got a remarkable result, that is, a path minimizing the Lagrangian action functional between two given…
Infinitely rising one-dimensional potentials constitute impenetrable barriers which reflect totally any incident wave. However, the scattering by such kind of potentials is not structureless: resonances may occur for certain values of the…