scholarly journals A Note on a Soluble Three?Body Problem

1965 ◽  
Vol 18 (2) ◽  
pp. 101 ◽  
Author(s):  
LM Delves
Keyword(s):  
Energy Spectrum ◽  
Helium Atom ◽  
Ground State ◽  
Bound States ◽  
Body Problem ◽  
Three Body Problem ◽  
Three Body

A class of soluble three-body systems suggested by Pluvinage is studied. The Hamiltonian Ho of these systems is not Hermitian, and the energy spectrum contains a continuum of bound states. The use of H 0 as a reference Hamiltonian in calculations of the helium atom ground state, as suggested by Pluvinage and Walsh, is discussed in the light of these results.

scholarly journals Three-body problem in 3D space: ground state, (quasi)-exact-solvability

2017 ◽  
Vol 50 (21) ◽  
pp. 215201 ◽  
Author(s):  
Alexander V Turbiner ◽  
Willard Miller ◽  
Adrian M Escobar-Ruiz
Keyword(s):  
Ground State ◽  
Body Problem ◽  
Three Body Problem ◽  
Exact Solvability ◽  
3D Space ◽  
Three Body

scholarly journals Relativistic oscillator model with spin for nucleon resonances

Open Physics ◽  
2013 ◽  
Vol 11 (8) ◽  
Author(s):  
Dmitry Kulikov ◽  
Ivan Uvarov ◽  
Arkadiy Yaroshenko
Keyword(s):  
Energy Spectrum ◽  
Total Energy ◽  
Body Problem ◽  
Oscillator Model ◽  
Three Body Problem ◽  
Regge Trajectories ◽  
Nucleon Resonances ◽  
Three Body ◽  
Relativistic Oscillator ◽  
Exact Energy

AbstractThe relativistic three-body problem is approached via the extension of the SL(2, C) group to the Sp(4, C) one. In terms of Sp(4, C) spinors, a Dirac-like equation with three-body kinematics is composed. After introducing the linear in coordinates interaction, it describes the spin-1/2 oscillator. For this system, the exact energy spectrum is derived and then applied to fit the Regge trajectories of baryon N-resonances in the (E 2, J) plane. The model predicts linear trajectories at high total energy E with some form of nonlinearity at low E.

An exactly soluble three-body problem in one dimension

1980 ◽  
Vol 58 (6) ◽  
pp. 719-728 ◽  
Author(s):  
C. Jung
Keyword(s):  
Closed Form ◽  
Bound States ◽  
Body Problem ◽  
Potential Functions ◽  
One Dimension ◽  
Three Body Problem ◽  
One Dimensional ◽  
Continuum States ◽  
Step Functions ◽  
Three Body

An exactly soluble one-dimensional three-body problem is presented, in which the interaction between the particles consists of local two-body potentials between each two particles. Infinitely high step functions are chosen for the form of the three potential functions. This interaction allows only three-body bound states and no continuum states. We have considered three different choices of the mass ratios of the three particles and we give formulas in closed form for the energies and for the wavefunctions of all states.

scholarly journals New Concept for Studying the Classical and Quantum Three-Body Problem: Fundamental Irreversibility and Time’s Arrow of Dynamical Systems

Particles ◽  
2020 ◽  
Vol 3 (3) ◽  
pp. 576-620
Author(s):  
A. S. Gevorkyan
Keyword(s):  
Dynamical System ◽  
Euclidean Space ◽  
Bound States ◽  
Body Problem ◽  
Local Coordinate System ◽  
Order System ◽  
Random Environments ◽  
Three Body Problem ◽  
Internal Time ◽  
Three Body

The article formulates the classical three-body problem in conformal-Euclidean space (Riemannian manifold), and its equivalence to the Newton three-body problem is mathematically rigorously proved. It is shown that a curved space with a local coordinate system allows us to detect new hidden symmetries of the internal motion of a dynamical system, which allows us to reduce the three-body problem to the 6th order system. A new approach makes the system of geodesic equations with respect to the evolution parameter of a dynamical system (internal time) fundamentally irreversible. To describe the motion of three-body system in different random environments, the corresponding stochastic differential equations (SDEs) are obtained. Using these SDEs, Fokker-Planck-type equations are obtained that describe the joint probability distributions of geodesic flows in phase and configuration spaces. The paper also formulates the quantum three-body problem in conformal-Euclidean space. In particular, the corresponding wave equations have been obtained for studying the three-body bound states, as well as for investigating multichannel quantum scattering in the framework of the concept of internal time. This allows us to solve the extremely important quantum-classical correspondence problem for dynamical Poincaré systems.

On the three-body problem

1973 ◽  
Vol 73 (1) ◽  
pp. 177-182 ◽  
Author(s):  
J. Lekner
Keyword(s):  
Ground State ◽  
Body Problem ◽  
Semiclassical Limit ◽  
Analytic Solutions ◽  
Equal Mass ◽  
Three Body Problem ◽  
Interacting Particles ◽  
Exact Ground State ◽  
General Force ◽  
Three Body

AbstractWe consider the ground state of a system of three interacting particles of equal mass. An integro-differential equation is obtained for the optimum pair function f in the product wavefunction Ψ(123) = f(12)f(13)f(23). The solution for harmonic forces reproduces the known exact ground state. Approximate analytic solutions are obtained for inverse-square forces, and for a general force law in the semiclassical limit.

Muonic helium atom as a classical three-body problem

2000 ◽  
Vol 62 (6) ◽  
pp. 7831-7841 ◽  
Author(s):  
T. J. Stuchi ◽  
A. C. B. Antunes ◽  
M. A. Andreu
Keyword(s):  
Helium Atom ◽  
Body Problem ◽  
Three Body Problem ◽  
Three Body
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