Related papers: Exact solutions for two-body problems in 1D deform…
We study deformations of the discrete Heisenberg group acting properly discontinuously on the Heisenberg group from the left and right and obtain a complete description of the deformation space.
The four-body bound state with two-body interactions is formulated in Three-Dimensional approach, a recently developed momentum space representation which greatly simplifies the numerical calculations of few-body systems without performing…
We study a three-body system, formed by a light particle and two identical heavy dipoles, in two dimensions in the Born-Oppenheimer approximation. We present the analytic light-particle wave function resulting from an attractive zero-range…
We develop a systematic procedure for constructing quantum many-body problems whose spectrum can be partially or totally computed by purely algebraic means. The exactly-solvable models include rational and hyperbolic potentials related to…
In this paper we will demonstrate that like the existence of a minimum measurable length, the existence of a maximum measurable momentum, also influence all quantum mechanical systems. Beyond the simple one dimensional case, the existence…
The relationship between the refractive index decrement, $\delta$, and the real part of the atomic form factor, $f^\prime$, is used to derive a simple polynomial functional form for $\delta(E)$ far from the K-edge of the element. The…
After a short review of the history and problems of relativistic Hamiltonian mechanics with action-at-a-distance inter-particle potentials, we study isolated two-body systems in the rest-frame instant form of dynamics. We give explicit…
A Hubbard-like model with SU(4) symmetry for electrons with two-fold orbital degeneracy is studied extensively. Exact solution in one dimension is derived by means of Bethe ansatz, where the sites are supposed to be occupied by at most two…
By splitting the Coulomb interaction into long-range and short-range components, we decompose the energy of a quantum electronic system into long-range and short-range contributions. We show that the long-range part of the energy can be…
The correlation between particle and wave descriptions of electron-matter interactions is analyzed by measuring the delocalization of an evanescent field using electron microscopy. Its spatial extension coincides with the energy-dependent,…
It is shown that the two-body Coulomb problem in the Sturm representation leads to a new two-dimensional, exactly-solvable, superintegrable quantum system in curved space with a $g^{(2)}$ hidden algebra and a cubic polynomial algebra of…
We provide a statistical and correlational analysis of the spatial and energetic properties of equilibrium configurations of a few-body system of two to eight equally charged classical particles that are confined on a one-dimensional…
This paper presents a fortran program to solve diverse few-body problems with the stochastic variational method. Depending on the available computational resources the program is applicable for $N=2-3-4-5-6-...$-body systems with $L=0$…
The solution of the hyperangular Schr\"odinger equation for few-body systems using a basis of explicitly correlated Gaussians remains numerically challenging. This is in part due to the number of basis functions needed as the system size…
The Effective One-Body formalism of the gravitational two-body problem in general relativity is reconsidered in the light of recent scattering amplitude calculations. Based on the kinematic relationship between momenta and the effective…
The two-body problem in general relativity is reduced to the problem of an effective particle (with an energy-dependent relativistic reduced mass) in an external field. The effective potential is evaluated from the Born diagram of the…
The equations for the electromagnetic two-body problem are neutral-delay equations that for generic initial data have solutions with discontinuous derivatives. If one wants to use these neutral-delay equations with arbitrary initial data,…
The methods of quantum chemistry and solid state theory to solve the many-body problem are reviewed. We start with the definitions of reduced density matrices, their properties (contraction sum rules, spectral resolutions, cumulant…
We formulate a method to study two-body correlations in a system of N identical bosons interacting via central two-body potentials. We use the adiabatic hyperspherical approach and assume a Faddeev-like decomposition of the wave function.…
The two-body Dirac equation with general local potential is reduced to the pair of ordinary second-order differential equations for radial components of a wave function. The class of linear + Coulomb potentials with complicated spin-angular…