Resolvent Operator Formulation of Stationary State Perturbation Theory

By starting with an exact operator equation and using different methods of expanding the resolvent operator, the Schrödinger, Wigner—Brilloin, similarity transformation, gauge transformation, and first-order perturbation iteration method, perturbation expansions are generated in a rigorous and straightforward manner. It is also shown how additional perturbation and perturbation iteration methods can be generated.