A resonance formulation for invariants of particle motion in a one- dimensional time-dependent potential (Q1062483)

A new ansatz for the functional form of invariants for the Hamiltonian \(H=p^ 2+V(q,t)\) is proposed and a formalism is developed for applying the ansatz. The dependence of an invariant on the momentum is represented by resonance denominators, where the locations of the resonances may be anywhere in the complex momentum plane. Previous results, which were obtained by diverse methods, are derived from a unified point of view within the context of this formulation. It may be possible to use the present work as the basis for a useful computational algorithm for solving self-consistent systems such as the Vlasov-Poisson equations.