On a general way of two-particle problem reduction

TL;DR

This paper introduces a general method to reduce the two-particle problem to a one-particle problem in an external potential, applicable in classical, non-relativistic, and relativistic quantum mechanics, based on the Maupertuis principle.

Contribution

It presents a novel, unified approach for simplifying two-particle problems across different physical regimes using the Maupertuis least action principle.

Findings

Method successfully reduces two-particle problems to one-particle problems.

Verified for classical mechanics, non-relativistic quantum mechanics, and relativistic quantum mechanics.

Provides a consistent framework applicable in various physical contexts.

Abstract

The problem of the description of two interacting particles is considered. It is shown that it can be reduced to the description of one particle in an external static potential even in a relativistic case. The method is based on the Maupertuis least action principle. The proposed method is verified for known problems in two-particle problems in classical mechanics, as well as in non-relativistic and relativistic quantum mechanics.