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