Related papers: Exact Quantum Solutions of Extraordinary N-body Pr…
An approximate quantum-mechanical two-body equation for spinless particles incorporating relativistic kinematics is derived. The derivation is based on the relativistic energy-momentum relation $mc^{2}+\epsilon =…
The Schr\"odinger-Poisson equations describe the behavior of a superfluid Bose-Einstein condensate under self-gravity with a 3D wave function. As $\hbar/m\to 0$, $m$ being the boson mass, the equations have been postulated to approximate…
We investigate ideal quantum gases in D-dimensional space and confined in a generic external potential by using the semiclassical approximation. In particular, we derive density of states, density profiles and critical temperatures for…
We calculate the renormalized effective 2-, 3-, and 4-body interactions for N neutral ultracold bosons in the ground state of an isotropic harmonic trap, assuming 2-body interactions modeled with the combination of a zero-range and…
Continuum structures of three short-range interacting particles in a deformed external one-body field are investigated. We use the equivalent $d$-method employing non-integer dimension, $d$, in a spherical calculation with a…
We study the electrodynamics of generic charged particles (bosons, fermions, relativistic or not) constrained to move on an infinite plane. An effective gauge theory in 2+1 dimensional spacetime which describes the real electromagnetic…
An exact treatment of the operators Q/e(\omega) and the total momentum is adopted to solve the nuclear matter Bruecker-Bethe-Goldstone equation with two- and three-body forces. The single-particle potential, equation of state and nucleon…
In the present work we solve the many-fermion problem in dimensions greater than one by identifying its normal modes. We start by decomposing the Fermi sea into independent sectors labeled by a wavevector q. The product of exactly…
This paper introduces a new difference scheme to the difference equations for N-body type problems. To find the non-collision periodic solutions and generalized periodic solutions in multi-radial symmetric constraint for the N-body type…
We study the quantum mechanics of the derivative nonlinear Schrodinger equation which has appeared in many areas of physics and is known to be classically integrable. We find that the N-body quantum problem is exactly solvable with both…
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…
Systems consisting of identical bosons with a large scattering length satisfy universal relations determined by 2-body physics that are similar to those for fermions with two spin states. They require the momentum distribution to have a…
The angular part of the Faddeev equations is solved analytically for s-states for two-body square-well potentials. The results are, still analytically, generalized to arbitrary short-range potentials for both small and large distances. We…
One of the oldest problems in physics is that of calculating the motion of $N$ particles under a specified mutual force: the $N$-body problem. Much is known about this problem if the specified force is non-relativistic gravity, and…
A nonlinear wave equation that describes different nonlinear effects in various fields of research was considered. In two particular cases, this equation was reduced to the Sine-Gordon equation and the Born-Infeld equation. Using the slowly…
The universal three-body dynamics in ultra-cold binary Fermi and Fermi-Bose mixtures is studied. Two identical fermions of the mass $m$ and a particle of the mass $m_1$ with the zero-range two-body interaction in the states of the total…
The exact solution of N- dimensional radial Schr\"odinger equation with the generalized Cornell potential has been obtained using the Laplace transformation (LT) method. The energy eigenvalues and the corresponding wave functions for any…
Thermodynamic properties of non-relativistic bosons and fermions in two spatial dimensions and without interactions are derived. All the virial coefficients are the same except for the second, for which the signs are opposite. This results…
We show the existence of Borromean bound states in a one-dimensional quantum three-body system composed of two identical bosons and a distinguishable particle. It is assumed that there is no interaction between the two bosons, while the…
We consider the many body quantum dynamics of systems of bosons interacting through a two-body potential $N^{3\beta-1} V (N^\beta x)$, scaling with the number of particles $N$. For $0< \beta < 1$, we obtain a norm-approximation of the…