相关论文: Two-body problem on a sphere. Reduction, stochasti…

The paper deals with an analytical study of various corrected Newtonian potentials. We offer a complete description of the corrected potentials, for the entire range of the parameters involved. These parameters can be fixed for different…

The problem of three particles interacting through harmonic forces is discussed within the Newtonian formalism. By means of a didactic approach, an exact analytical solution is found, and ways to extend it to the N-body case are pointed…

We describe a procedure to solve an up to $2N$ problem where the particles are separated topologically in $N$ groups with at most two particles in each. Arbitrary interactions are allowed between the (two) particles within one group. All…

We consider a pair of bosonic particles in a one-dimensional tight-binding periodic potential described by the Hubbard model with attractive or repulsive on-site interaction. We derive explicit analytic expressions for the two-particle…

Topology and geometry of a sphere create constraints for particles that lie on its surface which they otherwise do not experience in Euclidean space. Notably, the number of particles and the size of the system can be varied separately,…

The quantum mechanical many-body problem is rarely analytically solvable. One notable exception is the case of two electrons interacting via a Coulomb potential in a uniform magnetic field. The motion is confined to a two-dimensional plane,…

We investigate the relationship between rigid motions and relative equilibria in the N-body problem on the two-dimensional sphere, S2. We prove that any rigid motion of the N-body system on S2 must be a relative equilibrium. Our approach…

Analytic solutions of the quantum relativistic two-body problem are obtained for an interaction potential modeled as a one-dimensional smooth square well. Both stationary and moving pairs are considered and the limit of the…

A solvable many-body problem in the plane is exhibited. It is characterized by rotation-invariant Newtonian (``acceleration equal force'') equations of motion, featuring one-body (``external'') and pair (``interparticle'') forces. The…

Electron-electron correlation forms the basis of difficulties encountered in many-body problems. Accurate treatment of the correlation problem is likely to unravel some nice physical properties of matter embedded in this correlation. In an…

Natural orbital theory is a computationally useful approach to the few and many-body quantum problem. While natural orbitals are known and applied since many years in electronic structure applications, their potential for time-dependent…

The dynamics of a particle interacting with random classical field in a two-well potential is studied by the functional integration method. The probability of particle localization in either of the wells is studied in detail. Certain…

We consider the reduced two-body problem with a central potential on the sphere ${\bf S}^{2}$ and the hyperbolic plane ${\bf H}^{2}$. For two potentials different from the Newton and the oscillator ones we prove the nonexistence of an…

In this paper we provide an extension of the model discussed in [arXiv:1504.08283] describing two singularly interacting particles on the half-line. In this model, the particles are interacting only whenever at least one particle is…

We study the localization of particles rotating in a two-dimensional harmonic potential by solving their rotational spectrum using many-particle quantum mechanics and comparing the result to that obtained with quantizing the rigid rotation…

The correlated two-particle problem is solved analytically in the presence of a finite cavity. The method is demonstrated here in terms of exactly solvable models for both the cavity as well as the two-particle correlation where the…

We present a model for the motion of hard spherical particles on a two dimensional surface. The model includes both the interaction between the particles via collisions, as well as the interaction of the particles with the substrate. We…

We study a quantum mechanical system consisting of up to three identical dipoles confined to move along a helical shaped trap. The long-range interactions between particles confined to move in this one dimension leads to an interesting…

A simple one dimensional model is introduced describing a two particle "atom" approaching a point at which the interaction between the particles is lost. The wave function is obtained analytically and analyzed to display the entangled…

We introduce a restricted four body problem in a 2+2 configuration extending the classical Sitnikov problem to the Double Sitnikov problem. The secondary bodies are moving on the same perpendicular line to the planewhere the primaries…