Related papers: Heron Variables in 3-body Coulomb Problem
We consider the three-dimensional Dirac equation in spherical coordinates with coupling to static electromagnetic potential. The space components of the potential have angular (non-central) dependence such that the Dirac equation is…
In case of spinless particles there appear additional (singular) solutions in the framework of relativistic Klein-Gordon equation for Coulomb potential. These solutions obey to all requirements of quantum mechanical general principles.…
We develop a variational approach at finite temperature that incorporates many-body correlation self-consistently. The grand potential is constructed in terms of Green's function expressed by the variational parameters. We apply this…
Lowest bound S-state energy of Coulomb three-body systems ($N^{Z+}\mu^-e^-$) having a positively charged nucleus of charge number Z ($N^{Z+}$), a negatively charged muon ($\mu^-$) and an electron ($e^-$), is investigated in the framework of…
A new approach to the construction of difference schemes of any order for the many-body problem that preserves all its algebraic integrals is proposed. We introduced additional variables, namely, distances and reciprocal distances between…
A modification of Coulomb's law of friction uses a variable coefficient of friction that depends on a power law in the energy of mechanical oscillation. Through the use of three different exponents: 0, 1/2 and 1; all commonly encountered…
The exploration of entanglement and Bell non-locality among multi-particle quantum systems offers a profound avenue for testing and understanding the limits of quantum mechanics and local real hidden variable theories. In this work, we…
We prove a priori bounds for all derivatives of non-relativistic Coulombic eigenfunctions, involving negative powers of the distance to the singularities of the many-body potential. We use these to derive bounds for all derivatives of the…
The classical three-body harmonic system in $\mathbb{R}^d$ ($d>1$) with finite rest lengths and zero total angular momentum $L=0$ is considered. This model describes the dynamics of the $L=0$ near-equilibrium configurations of three point…
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 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…
Loop variables are used to describe the presence of topological defects in spacetime. In particular we study the dependence of the holonomy transformation on angular momentum and torsion for a multi-chiral cone. We also compute the…
We formulate two methods to facilitate the calculation of perturbative corrections to quantum few-body observables. Both techniques are designed for a numerical realization in combination with any tool that obtains either the entire…
Using the approach the modified Euler-Lagrange field equation together with the corresponding Seiberg-Witten maps of the dynamical fields, a noncommutative Dirac equation with a Coulomb potential is derived. We then find the noncommutative…
We consider a model of three electrons and one hole confined in a two-dimensional (2D) plane, interacting with one another through Coulomb forces. Using a Ritz variational method we find an upper bound of \approx -0.0112me^4/8\pi^2 \epsilon…
Universal low-energy properties are studied for three identical bosons confined in two dimensions. The short-range pair-wise interaction in the low-energy limit is described by means of the boundary condition model. The wave function is…
Coulomb wave functions are difficult to compute numerically for extremely low energies, even with direct numerical integration. Hence, it is more convenient to use asymptotic formulas in this region. It is the object of this paper to derive…
Efficient simulation of many-body quantum systems is central to advances in physics, chemistry, and quantum computing, with a key question being whether the simulation cost scales polynomially with the system size. In this work, we analyze…
We investigate dissociation reactions of loosely bound and spatially extended three-body systems. We formulate a practical method for simultaneous treatment of long-range Coulomb and short-range nuclear interactions. We use $^6$He…
There are two fundamental problems studied by the theory of hamiltonian integrable systems: integration of equations of motion, and construction of action-angle variables. The third problem, however, should be added to the list: separation…