  The Eriksen method is proven to yield a correct and exact result when a
sufficient condition of exact transformation to the Foldy-Wouthuysen (FW)
representation is satisfied. Therefore, the Eriksen method is confirmed as
valid. This makes it possible to establish the limits within which the
approximate "step-by-step" methods are applicable. The latter is done by
comparing the relativistic formulas for a Hamiltonian operator in the FW
representation (obtained using those methods) and the known expression for the
first terms of a series, which defines the expansion of this operator in powers
of v/c as found by applying the Eriksen method.
