An exactly solvable one‐dimensional three‐body problem with hard cores

1980 ◽  
Vol 21 (5) ◽  
pp. 1083-1085 ◽  
Author(s):  
Robert Nyden Hill
Keyword(s):  
Body Problem ◽  
Three Body Problem ◽  
One Dimensional ◽  
Exactly Solvable ◽  
Three Body

The quasi-exactly solvable potentials method applied to the three-body problem

2007 ◽  
Vol 322 (5) ◽  
pp. 1034-1042 ◽  
Author(s):  
F. Chafa ◽  
A. Chouchaoui ◽  
M. Hachemane ◽  
F.Z. Ighezou
Keyword(s):  
Body Problem ◽  
Three Body Problem ◽  
Solvable Potentials ◽  
Exactly Solvable Potentials ◽  
Exactly Solvable ◽  
Three Body

PERIODIC ORBITS NEAR A HETEROCLINIC LOOP FORMED BY ONE-DIMENSIONAL ORBIT AND A TWO-DIMENSIONAL MANIFOLD: APPLICATION TO THE CHARGED COLLINEAR THREE-BODY PROBLEM

2007 ◽  
Vol 17 (06) ◽  
pp. 2175-2183
Author(s):  
JAUME LLIBRE ◽  
DANIEL PAŞCA
Keyword(s):  
Periodic Orbits ◽  
Degrees Of Freedom ◽  
Body Problem ◽  
Negative Energy ◽  
Dimensional Manifold ◽  
Three Body Problem ◽  
Heteroclinic Loop ◽  
One Dimensional ◽  
Three Body ◽  
Total Collision

This paper is devoted to the study of a type of differential systems which appear usually in the study of the Hamiltonian systems with two degrees of freedom. We prove the existence of infinitely many periodic orbits on each negative energy level. All these periodic orbits pass near to the total collision. Finally we apply these results to study the existence of periodic orbits in the charged collinear three-body problem.

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.

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