Foldy-Wouthyusen wave functions and conditions of transformation between Dirac and Foldy-Wouthuysen representations

TL;DR

This paper establishes the precise conditions needed to transform Dirac wave functions into the Foldy-Wouthuysen representation, enabling better calculation of classical quantities from quantum wave functions.

Contribution

It formulates and proves the conditions for the transformation between Dirac and FW representations, clarifying the connection between their wave functions.

Findings

Derived conditions for Dirac to FW transformation.

Established the relation between wave functions in both representations.

Enabled calculation of classical expectation values from quantum states.

Abstract

The block-diagonalization of the Hamiltonian is not sufficient for the transformation to the Foldy-Wouthuysen (FW) representation. The conditions enabling the transition from the Dirac representation to the FW one are formulated and proved. The connection between wave functions in the two representations is derived. The results obtained allows calculating expectation values of operators corresponding to main classical quantities.