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Exact integrodifferential equation for the ground state of an N-body system interacting with the help of a two-body potential

M. Fabre de la Ripelle, H. Fiedeldey

Published Apr 1, 1986• 0 citations
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In this work, a direct solution to the few-body Integrodifferential equation using the Lagrange-mesh method is presented.With the Lagrange-mesh method, the few-body Integrodifferential equation is converted into a matrix eigenvalue problem for numerical treatment.The accuracy and stability of the solution is tested by calculating groundstate binding energies for few-boson systems interacting via the Ali-Bodmer, Volkov and Malfliet-Tjon (MTV) nuclear potentials for A-body systems (where A = 4, 5, 6, 7).A rapid convergence of the results is achieved and calculated ground-state energies are in good agreement with those available in the literature, where different approaches were used.The method is promising and could be extended to larger number of particles such as those involved in the Bose-Einstein condensates.
A new microscopic approach to the theory of dynamic correlation, ground state and collective excitations of many‐body systems is suggested. These dynamic and ground state properties are known as being interconnected and should be considered on the same base. A useful tool for this goal is a response function formalism. An exact functional equation for effective interaction and linear response function is obtained. The reduction method of the functional equation to a closed set of equations is given. In the simplest case the functional equation may be transformed into nonlinear integrodifferential equation. Few examples of many‐body systems are considered on the base of this equation. The developed method is applied to gas‐liquid phase transition, for evaluation of transport coefficients and collective excitation width.