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The set of Faddeev and Lippmann--Schwinger integral equations for three-body systems involving Coulomb interactions deduced from a ``three-potential'' picture are shown to be compact for all energies and a method of solution is given.

Nuclear Theory · Physics 2007-05-23 Z. Papp

We use Dirac's constraint dynamics to obtain a Hamiltonian formulation of the relativistic N-body problem in a separable two-body basis in which the particles interact pair-wise through scalar and vector interactions. The resultant N-body…

Nuclear Theory · Physics 2009-11-06 Cheuk-Yin Wong , Horace W. Crater

We present analytical solutions to a quantum-mechanical three-body problem in three dimensions, which describes a helium-like two-electron atom. Similarly to Hooke's atom, the Coulombic electron-nucleus interaction potentials are replaced…

Quantum Physics · Physics 2017-02-15 C. A. Downing

Gravitational and electromagnetic interactions are Hamiltonian systems with forces between pairs of particles. We propose an alternative: Hamiltonian dynamics with triplet interactions between point particles. Our system has a potential…

Chaotic Dynamics · Physics 2025-07-22 J. D. Meiss

In this note we discuss the quantum mechanical three-body problem with pairwise zero-range interactions in dimension three. We review the state of the art concerning the construction of the corresponding Hamiltonian as a self-adjoint…

Mathematical Physics · Physics 2016-02-01 Giulia Basti , Alessandro Teta

The constant pairing Hamiltonian holds exact solutions worked out by Richardson in the early Sixties. This exact solution of the pairing Hamiltonian regained interest at the end of the Nineties. The discret complex-energy states had been…

Mathematical Physics · Physics 2017-07-12 Rodolfo M. Id Betan

We analyze the dynamics between 1/$\lambda$-fractional statistics particles (anyons) in an exact three-body solution of the Sutherland Hamiltonian. We show that anyons interact by means of a short-range attraction. The interaction dictates…

Strongly Correlated Electrons · Physics 2007-05-23 B. A. Bernevig , D. Giuliano , D. I. Santiago

In this work we study 2- and 3-body oscillators with quadratic and sextic pairwise potentials which depend on relative distances, $|{\bf r}_i - {\bf r}_j |$, between particles. The two-body harmonic oscillator is two-parametric and can be…

Mathematical Physics · Physics 2021-09-23 Alexander V Turbiner , Willard Miller , Adrian M Escobar-Ruiz

We give a self-contained presentation and comparison of two different algorithms to explicitly solve quantum many body models of indistinguishable particles moving on a circle and interacting with two-body potentials of $1/\sin^2$-type. The…

Mathematical Physics · Physics 2015-06-26 Edwin Langmann

Recent work in the literature has studied the restricted three-body problem within the framework of effective-field-theory models of gravity. This paper extends such a program by considering the full three-body problem, when the Newtonian…

General Relativity and Quantum Cosmology · Physics 2014-10-17 Emmanuele Battista , Giampiero Esposito

A method of solving the Schr\"{o}dinger equation based on the use of constant particle-particle interaction potential surfaces (IPS) is proposed. The many-body wave function is presented in a configuration interaction form, with…

Computational Physics · Physics 2016-04-20 V. M. Tapilin

We investigate the prospects of combining a standard momentum space approach for ultracold three-body scattering with efficient coordinate space schemes to solve the underlying two-body problem. In many of those schemes the two-body problem…

Quantum Gases · Physics 2021-03-17 T. Secker , J. -L. Li , P. M. A. Mestrom , S. J. J. M. F. Kokkelmans

Several N-body problems in ordinary (3-dimensional) space are introduced which are characterized by Newtonian equations of motion (``acceleration equal force;'' in most cases, the forces are velocity-dependent) and are amenable to exact…

Mathematical Physics · Physics 2015-06-26 Massimo Bruschi , Francesco Calogero

Three-body interactions have been measured among three charged colloidal particles in deionized solvent. Two of the particles have been confined to an optical line-trap while the third one was approached by means of a focused laser beam.…

Soft Condensed Matter · Physics 2008-01-28 M. Brunner , J. Dobnikar , H. H. von Grünberg , C. Bechinger

We show that polar molecules driven by microwave fields give naturally rise to strong three-body interactions, while the two-particle interaction can be independently controlled and even switched off. The derivation of these effective…

Statistical Mechanics · Physics 2015-06-25 H. P. Büchler , A. Micheli , P. Zoller

This is the second article in a series where we succeed in enlarging the class of solvable problems in one and three dimensions. We do that by working in a complete square integrable basis that carries a tridiagonal matrix representation of…

Mathematical Physics · Physics 2015-05-18 A. D. Alhaidari

The system is described by three mass-shell constraints. After a nonlinear transformation of the momenta, the analytic form taken by admissible interactions (allowing compatibility) is characterized in terms of the new variables. These…

High Energy Physics - Phenomenology · Physics 2009-11-11 Philippe Droz-Vincent

The $\eta$-3N-interaction is studied within the four-body Faddeev-Yakubovsky theory adopting purely separable forms for the two- and three-body subamplitudes, limiting the basic two-body interactions to s-waves only. The corresponding…

Nuclear Theory · Physics 2009-11-07 A. Fix , H. Arenhoevel

It is known that three-body contact interactions in one-dimensional $n(\geq3)$-body problems of nonidentical particles can be topologically nontrivial: they are all classified by unitary irreducible representations of the pure twin group…

Quantum Physics · Physics 2024-01-23 Satoshi Ohya

An approach is developed to find approximate solutions to the restricted circular three body problem. The solution is useful in approximately describing the position vectors of three spherically symmetric masses, one of which has a much…

Mathematical Physics · Physics 2007-05-23 Abu Bakr Mehmood , S. Umer Abbas , Ghulam Shabbir