Related papers: Low-lying spectra in anharmonic three-body oscilla…
The three-body problem in one-dimension with a repulsive inverse square potential between every pair was solved by Calogero. Here, the known results of supersymmetric quantum mechanics are used to propose a number of new three-body…
A new convenient method to diagonalize the non-relativistic many-body Schroedinger equation with two-body central potentials is derived. It combines kinematic rotations (democracy transformations) and exact calculation of overlap integrals…
We show that the single quasi-particle Schr\"odinger equation for a certain form of one-body potential yields a stationary one soliton solution. The one-body potential is assumed to arise from the self- interacting charge distribution with…
For any central potential V in D dimensions, the angular Schroedinger equation remains the same and defines the so called hyperspherical harmonics. For non-central models, the situation is more complicated. We contemplate two examples in…
With a number of special Hamiltonians, solutions of the Schr\"{o}dinger equation may be found by separation of variables in more than one coordinate system. The class of potentials involved includes a number of important examples, including…
We quantize the 1-dimensional 3-body problem with harmonic and inverse square pair potential by separating the Schr\"odinger equation following the classic work of Calogero, but allowing all possible self-adjoint boundary conditions for the…
The three-body Schr\"{o}dinger operator in the space of square integrable functions is found to be a certain extension of operators which generate the exponential unitary group containing a subgroup with nilpotent Lie algebra of length…
The spherical reduction of the rational Calogero model (of type $A_{n-1}$ and after removing the center of mass) is considered as a maximally superintegrable quantum system, which describes a particle on the $(n{-}2)$-sphere subject to a…
As a straightforward generalization and extension of our previous paper, J. Phys. A50 (2017) 215201 we study aspects of the quantum and classical dynamics of a $3$-body system with equal masses, each body with $d$ degrees of freedom, with…
A new exactly solvable alternative to the Calogero three-particle model is proposed. Sharing its confining long-range part, it contains the mere zero-range two-particle barriers. Their penetrability gives rise to a tunneling, tunable via…
This work is devoted to the study of some exactly solvable quantum problems of four, five and six bodies moving on the line. We solve completely the corresponding stationary Schr\"odinger equation for these systems confined in an harmonic…
A distorted-wave version of the renormalisation group is applied to scattering by an inverse-square potential and to three-body systems. In attractive three-body systems, the short-distance wave function satisfies a Schroedinger equation…
In this paper, we determine at weak coupling the non-relativistic $n$-body Schr\"{o}dinger equation that describes the low-lying color singlet bound states of two dimensional adjoint $QCD$ with heavy quarks. In the case of three adjoint…
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…
We study a heavy-heavy-light three-body system confined to one space dimension. Both binding energies and corresponding wave functions are obtained for (i) the zero-range, and (ii) two finite-range attractive heavy-light interaction…
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…
We consider the spherical reduction of the rational Calogero model (of type $A_{n-1}$, without the center of mass) as a maximally superintegrable quantum system. It describes a particle on the $(n{-}2)$-sphere in a very special potential. A…
We study the Schr\"{o}dinger equation with $1/r^3$ and attractive $1/r^2$ potentials. Using the quantum defect theory, we obtain analytical solutions for both repulsive and attractive $1/r^3$ interactions. The obtained…
Schroedinger bound-state problem in D dimensions is considered for a set of central polynomial potentials (containing 2q coupling constants). Its polynomial (harmonic-oscillator-like, quasi-exact, terminating) bound-state solutions of…
We study aspects of the quantum and classical dynamics of a $3$-body system in 3D space with interaction depending only on mutual distances. The study is restricted to solutions in the space of relative motion which are functions of mutual…