COMPLEMENTARY BOUNDS FOR DYNAMIC POLARIZABILITIES

Complementary variational principles are developed for ground-state wave function corrections which are induced by frequency-dependent perturbations. These principles lead to upper and lower bounds for dynamic polarizabilities which are either measured at real frequencies less in magnitude than the first excitation energy, or measured at any imaginary frequencies. In the latter case there is a choice of upper bounds, different forms being suited to small and large frequencies. Illustrative results are presented for the hydrogen atom, and reasonable accuracy is obtained with simple one-parameter trial functions.