Variational Methods in the Wave Operator Formalism. A Unified Treatment for Bound and Quasibound Electronic and Molecular States

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Abstract
The wave operator formalism of Löwdin, heretofore used to describe states belonging to the discrete energy spectrum, has been extended to unify the treatment of bound and quasibound (or decaying) states. The approach makes use of an arbitrary reference function that may be chosen to approximate the physical state at short distances. Real and complex eigenvalues are obtained, respectively, for bound and quasibound states from an implicit equation, valid for all coupling strengths. Resonance positions and linewidths are explicitly independent of energy. Variational principles of the Lippmann—Schwinger type are presented which apply to states with either bound‐state or decay boundary conditions. Particular cases leading to minimization or maximization principles for real energies are discussed. The formalism is considered in connection with decaying electronic states of atoms and decaying molecular states.

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