General properties of the Foldy-Wouthuysen transformation and applicability of the corrected original Foldy-Wouthuysen method

TL;DR

This paper analyzes the properties of the Foldy-Wouthuysen transformation, identifies limitations of the original method, and proposes a correction algorithm using the Baker-Campbell-Hausdorff formula, with applicability constrained by convergence conditions.

Contribution

It introduces a correction approach for the original Foldy-Wouthuysen transformation using the Baker-Campbell-Hausdorff formula and discusses its applicability and limitations.

Findings

The original method does not satisfy the Eriksen condition.

A correction algorithm for the transformation is proposed.

Applicability is limited by convergence of relativistic series.

Abstract

General properties of the Foldy-Wouthuysen transformation which is widely used in quantum mechanics and quantum chemistry are considered. Merits and demerits of the original Foldy-Wouthuysen transformation method are analyzed. While this method does not satisfy the Eriksen condition of the Foldy-Wouthuysen transformation, it can be corrected with the use of the Baker-Campbell-Hausdorff formula. We show a possibility of such a correction and propose an appropriate algorithm of calculations. An applicability of the corrected Foldy-Wouthuysen method is restricted by the condition of convergence of a series of relativistic corrections.