A small parameter approach 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 ratio of potential to kinetic energy, simplifying calculations for states with higher quantum numbers.

Contribution

It develops a novel small parameter expansion technique that reduces the complexity of few-body problem solutions by incorporating high-energy states in a closed form.

Findings

Efficient approximation for high quantum number states.

Perturbative reduction to finite-dimensional subspace.

Closed-form inclusion of contributions from large K states.

Abstract

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