Hierarchy of Sum Rules for Oscillator Strengths

Abstract: It is shown that the well known sum rules for oscillator strengths for Hydrogen atom can be generalised to a whole class of sum rules. The sum rules have contributions from the discrete and the continuum parts of the spectrum neither of which can be calculated in closed analytical form but can be calculated numerically. The numerical calculations are carried out to check the validity of the sum rules. The procedure for constructing sum rules for general potentials is discussed. Generalisations of Kramers relations and the Virial theorem are discussed.