scholarly journals Three-body problem in d-dimensional space: Ground state, (quasi)-exact-solvability

2018 ◽  
Vol 59 (2) ◽  
pp. 022108 ◽  
Author(s):  
Alexander V. Turbiner ◽  
Willard Miller ◽  
M. A. Escobar-Ruiz
Keyword(s):  
Ground State ◽  
Body Problem ◽  
Dimensional Space ◽  
Three Body Problem ◽  
Exact Solvability ◽  
Three Body

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 Four-body problem in d-dimensional space: Ground state, (quasi)-exact-solvability. IV

2019 ◽  
Vol 60 (6) ◽  
pp. 062101 ◽  
Author(s):  
M. A. Escobar-Ruiz ◽  
Willard Miller ◽  
Alexander V. Turbiner
Keyword(s):  
Ground State ◽  
Body Problem ◽  
Dimensional Space ◽  
Exact Solvability ◽  
Four Body Problem

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.

Three-body problem of two electron atoms. II

1980 ◽  
Vol 58 (6) ◽  
pp. 760-762 ◽  
Author(s):  
S. G. Lie ◽  
Y. Nogami
Keyword(s):  
Wave Function ◽  
Correlation Function ◽  
Electron Correlation ◽  
Ground State ◽  
Short Range ◽  
Body Problem ◽  
Ground State Wave Function ◽  
Three Body Problem ◽  
State Wave ◽  
Three Body

With the ansatz that the ground state wave function for a helium-like atom is of the form of [Formula: see text], the optimal correlation function [Formula: see text] is determined. Here x and y are the distances of the electrons from the nucleus, while z is that between the electrons. The parameters α and β are determined by minimizing the energy of the system. The method is particularly useful for calculating quantities which are sensitive to the short-range electron–electron correlation.

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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