Generalizations of the Jost Functions

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Abstract
The Jost functions have proved valuable in the study of the analytic properties of the scattering phase for the radial Schrödinger equation. In the present paper we shall present an alternative definition of the Jost functions, prove the equivalence of the new definition to the usual one, and generalize the new definition to the one‐dimensional Schrödinger equation (− ∞ <x< ∞), the three‐dimensional nonseparated Schrödinger equation, and the three‐dimensional nonseparated Dirac equation. It is hoped that these generalizations lead to a better understanding of the analytic properties of the scattering operator for these and related dynamical systems. The generalized Jost functions are shown to be operators in the variables which label the degeneracy of the continuous spectrum of the Hamiltonians which are considered.