Some properties of bound states in the three-body problem with separable potentials

1971 ◽  
Vol 21 (9) ◽  
pp. 923-929 ◽  
Author(s):  
V. I. Kukulin
Keyword(s):  
Bound States ◽  
Body Problem ◽  
Three Body Problem ◽  
Separable Potentials ◽  
Three Body

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.

Three-Body Problem with Separable Potentials. II.n−dScattering

1963 ◽  
Vol 131 (3) ◽  
pp. 1265-1271 ◽  
Author(s):  
A. N. Mitra ◽  
V. S. Bhasin
Keyword(s):  
Body Problem ◽  
Three Body Problem ◽  
Separable Potentials ◽  
Three Body

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.

Rigid-Rotator and Fixed-Shape Solutions to the Coulomb Three-Body Problem

1997 ◽  
Vol 22 (1) ◽  
pp. 37-60 ◽  
Author(s):  
A. Santander ◽  
J. Mahecha ◽  
F. Pérez
Keyword(s):  
Body Problem ◽  
Three Body Problem ◽  
Rigid Rotator ◽  
Three Body
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