A Small Parameter Method for Few-Body Problems

TL;DR

This paper introduces a perturbative method for solving few-body quantum problems by expanding over a small parameter related to the energy ratio, simplifying calculations for complex systems.

Contribution

It develops a novel small parameter expansion technique that reduces the complexity of few-body problems without expanding over basis functions.

Findings

Efficiently reduces the dimensionality of the problem.

Provides a closed-form contribution from high-energy subspaces.

Applicable to various few-body quantum systems.

Abstract

A procedure to solve few-body problems which is based on an expansion over a small parameter is developed. The parameter is the ratio of potential energy to kinetic energy in the subspace of states having not small hyperspherical quantum numbers, K>K_0. Dynamic equations are reduced perturbatively to those in the finite subspace with K \le K_0. The contribution from the subspace with K>K_0 is taken into account in a closed form, i.e. without an expansion over basis functions.