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The paper describes conditions for transformation from the Diracrepresentation to the Foldy-Wouthuysen representation. The necessary conditionis the block-diagonal transformation of Hamiltonian relative to the upper andlower components of the wave function. The sufficient condition is the wavefunction transformation law described by relation (6). It has been demonstratedthat the unitary transformations offered by the authors of the papers [14],[15], [16], [17] do not satisfy the sufficiency condition (6) and, hence, theyare not the Foldy-Wouthuysen transformations. In applications, the matrixelements of any operator in the FW representation can be calculated, accordingto (6), using the normalized two-component wave functions in the Diracrepresentation known for the given problem.

The Necessary and Sufficient Conditions for Transformation from Dirac Representation to Foldy-Wouthuysen Representation