On the possibility of an analytic solution of the three-body problem

✍ Scribed by V.B Mandelzweig

• Publisher: Elsevier Science
• Year: 1977
• Tongue: English
• Weight: 915 KB
• Volume: 104
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1016/0003-4916(77)90043-4

✦ Synopsis

Three-body Faddeev equations in the Noyes-Fiedeldey form are rewritten as a matrix analog of a one-dimensional nonrelativistic SchrGdinger equation. Unlike the method of K-harmonics, where a similar equation was obtained by expansion of a three-body Schrijdinger equation wavefunction into the orthogonal set of functions of two variables (K-harmonics), the use of the Noyes-Fiedeldey form of Faddeev equations allows us to limit ourselves to the expansion in functions of one variable only. The solutions of the above mentioned matrix equation are obtained. These solutions converge uniformly within every interval of continuity of the matrix, which corresponds to the potential of that equation. Their asymptotic behavior for large interparticle distances is discussed. The solutions for the harmonic oscillator, inverse-square, and Coulomb-Kepler potentials are found. It is shown that energy levels in the last case may be calculated from a simple formula which is very similar to the corresponding formula for the two-body Coulomb-Kepler problem. This formula can be easily generalized to the case of n particles interacting with inverse distance potentials.