Improved Method For Quantum Mechanical Three Body Problems

The quantum-mechanical ground-state problem for three identical particles bound by attractive inter-particle potentials is discussed. For this problem it has previously been shown that it is advantageous to write the wave function in a special functional form, form which an integral equation which is equivalent to the Schrodinger equation was derived. In this paper a new method for solving this equation is presented. The method involves an expansion of a two-body problem with a potential of the same shape as the inter-particle potential in the three-body problem, but of enhanced strength.

The Quantum Mechanical Three-Body Problem deals with the three-body problem in quantum mechanics. Topics include the two- and three-particle problem, the Faddeev equations and their solution, separable potentials, and variational methods. This book has eight chapters; the first of which introduces the reader to the quantum mechanical three-body problem, its difficulties, and its importance in nuclear physics. Scattering experiments with three-particle breakup are presented. Attention then turns to some concepts of quantum mechanics, with emphasis on two-particle scattering and the Hamiltonian for three particles. The chapters that follow are devoted to the Faddeev equations, including those for scattering states and transition operators, and how such equations can be solved in practice. The solution of the Faddeev equations for separable potentials and local potentials is presented, along with the use of Padé approximation to solve the Faddeev equations. This book concludes with an appraisal of variational methods for bound states, elastic and rearrangement scattering, and the breakup reaction. A promising variational method for solving the Faddeev equations is described. This book will be of value to students interested in three-particle physics and to experimentalists who want to understand better how the theoretical data are derived.

This bibliography lists all in-house reports, journal articles, and contractor reports issued from 1 July 1966 to 30 September 1967. Part I lists all in-house reports by the series in which they were issued; Part II lists all in-house reports, journal articles, and contractor reports by the Laboratory responsible for their preparation. In Part I, the reports are listed numerically by series; in Part II, in-house reports and journal articles are listed alphabetically by author, and contractor reports are listed numerically by the AFCRL report number.