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A formulation in terms of projection operators of the Van Vleck trans-formation is presented. Explicit formulae through eighth order are given, and the eleventh order may be reached fairly simply. Such high orders are relevant for the Born-Oppenheimer separation. It is proved that the Van Vleck transformation conserves symmetry. A special formulation is given for product spaces. The Foldy-Wouthuysen transformation is treated as an example.
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Jørgensen et al. (1974) studied this question.
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