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Relativistic methods for the Foldy-Wouthuysen transformation of the``step-by-step'' type already at the first step give an expression for theHamilton operator not coinciding with the exact result determined by theEriksen method. The methods agree for the zeroth and first orders in the Planckconstant terms but do not agree for the second and higher-order terms. Weanalyze the benefits and drawbacks of various methods and establish theirapplicability boundaries.

Comparative analysis of direct and "step-by-step" Foldy-Wouthuysen transformation methods