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

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 proven. The connection between wave functions in the two representations is derived. The results obtained allow calculating expectation values of operators corresponding to main classical quantities.

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