Related papers: Exact Solution of a N-body Problem in One Dimensio…

We explore the connection between quantum entanglement and the exchange symmetry of the states of N identical particles. Each particle has n-levels. The N particles span the nN dimensional Hilbert space. We shall call the general state of…

Motivated by the recent article of P. Shea {\it et al.} [Am. J. Phys. {\bf 77} (6), 2009] we examine the exactly solvable problem of two harmonically trapped ultra-cold bosonic atoms interacting {\it via} a short range potential in one and…

Closed formulas for tree amplitudes of $n$-particle scatterings of gluon, graviton, and massless scalar particles have been proposed by Cachazo, He, and Yuan. It depends on $(n-3)$ quantities $\s_\a$ which satisfy a set of coupled {\it…

Consider n=2l>=4 point particles with equal masses in space, subject to the following symmetry constraint: at each instant they form an orbit of the dihedral group D_l, where D_l is the group of order 2l generated by two rotations of angle…

The integrability of one dimensional quantum mechanical many-body problems with general contact interactions is extensively studied. It is shown that besides the pure (repulsive or attractive) $\delta$-function interaction there is another…

This is the second in a pair of articles that classify the configuration space and kinematic symmetry groups for $N$ identical particles in one-dimensional traps experiencing Galilean-invariant two-body interactions. These symmetries…

We consider the stability problem for a unitary N+1 fermionic model, i.e., a system of $N$ identical fermions interacting via zero-range interactions with a different particle, in the case of infinite two-body scattering length. We present…

A new class of solvable $N$-body problems is identified. They describe $N$ unit-mass point particles whose time-evolution, generally taking place in the complex plane, is characterized by Newtonian equations of motion "of goldfish type"…

Scattering and bound states for a spinless particle in the background of a kink-like smooth step potential, added with a scalar uniform background, are considered with a general mixing of vector and scalar Lorentz structures. The problem is…

This paper addresses the question, whether the solutions of the scattering equations in four space-time dimensions can be expressed as rational functions of the momentum twistor variables. This is the case for $n\le5$ external particles.…

The N-dimensional radial Schrodinger equation with an extended Cornell potential is solved. The analytical exact iteration method is applied. The energy eigenvalues are calculated in the N-dimensional space. The charmonium meson, the…

Considering two-body integral equations we show how they can be dimensionally reduced by integrating exactly over the azimuthal angle of the intermediate momentum. Numerical solution of the resulting equation is feasible without employing a…

We derive exact relations for $N$ spin-1/2 fermions with zero-range or short-range interactions, in continuous space or on a lattice, in $2D$ or in $3D$, in any external potential. Some of them generalize known relations between 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…

Consider a system of $N$ bosons in three dimensions interacting via a repulsive short range pair potential $N^2V(N(x_i-x_j))$, where $\bx=(x_1, >..., x_N)$ denotes the positions of the particles. Let $H_N$ denote the Hamiltonian of the…

This is the first in a pair of articles that classify the configuration space and kinematic symmetry groups for $N$ identical particles in one-dimensional traps experiencing Galilean-invariant two-body interactions. These symmetries explain…

We have previously studied properties of a one-dimensional potential with $N$ equally spaced identical barriers in a (fixed) finite interval for both finite and infinite $N$. It was observed that scattering and spectral properties depend…

Using the coordinate transformation method, we solve the one-dimensional Schr\"{o}dinger equation with position-dependent mass(PDM). The explicit expressions for the potentials, energy eigenvalues and eigenfunctions of the systems are…

We study the lowest energy E of a relativistic system of N identical bosons bound by pair potentials of the form V(r_{ij}) = g(r_{ij}^2) in three spatial dimensions. In natural units hbar = c = 1 the system has the semirelativistic…

With the use of the general covariant matrix 10-dimensional Petiau -- Duffin -- Kemmer formalism in cylindrical coordinates and tetrad there are constructed exact solutions of the quantum-mechanical equation for a particle with spin 1 in…