Generalization of the Lagrange equilateral-triangle solution and the Euler collinear solution to nongravitational forces in the three-body problem

Details Generalization of the Lagrange equilateral-triangle solution and the Euler collinear solution to nongravitational forces in the three-body problem Generalization of the Lagrange equilateral-triangle solution and the Euler collinear solution to nongravitational forces in the three-body problem

Feb 1978

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1978phrvd..17..976c&link_type=abstract

Physical Review D - Particles and Fields, 3rd Series, vol. 17, Feb. 15, 1978, p. 976-984.

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3

Gravitational Effects, Particle Interactions, Quantum Mechanics, Three Body Problem, Atomic Energy Levels, Coulomb Potential, Hamiltonian Functions, Helium

Scientific paper

In the gravitational three-body problem there are special configurations that allow exact solutions. They are the equilateral-triangle and collinear configurations. This paper shows that exact solutions for these special configurations and others as well exist for forces other than gravitational. The interactions include 'scalar' forces or those derived from a world scalar potential as well as Coulomb or 'vector' forces. In the formalism used for this classical treatment the aspects emphasized are those which can be carried over to quantum mechanics. An application to an atomic system yields a reasonable estimate of the energy levels for heliumlike atoms.

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