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Physical Review C

Exact solution of the four-body Faddeev-Yakubovsky equations for the harmonic oscillator

Alexander L. Zubarev, Victor B. Mandelzweig

Published Jul 1, 1994• 4 citations
Publisher

Abstract

The Faddeev-Yakubovsky equations for four identical spinless particles in three-dimensional space interacting via harmonic-oscillator two-body potentials are solved analytically for any excitation and for an arbitrary value of the total angular momentum.
DOI
10.1103/physrevc.50.38

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The quantization of orbital angular momentum can be introduced simply through the model of the two- and three-dimensional simple harmonic oscillator. Most of the analysis is carried out in the familiar Cartesian coordinate system in which the simple harmonic oscillator Schrödinger equation is separable. Angular momentum eigenfunctions are constructed by superposition, and the resulting functions easily transformed into spherical coordinates. The angle-dependent parts of the solutions are the spherical harmonics, which are the orbital angular momentum eigenfunctions for all central potentials including the Coulomb potential of the hydrogen atom. The method also introduces the separation of variables technique and provides practice in applying the concepts of completeness, orthogonality, superposition of states, and alternative representations.