Hamilton-Jacobi/action-angle-variable theory of scattering

Abstract

<p>The classical and quantum action variable theory is extended to scattering by defining the action variable for the scattering region such that the new definition is consistent with the definition given earlier for the eigenstates. The forms of both the classical and the quantum action variables are maintained for both off-eigenstates and scattering states. The location of the turning points is studied in order to define the classical action variable and the location of the poles of the quantum momentum function is studied in order to define the quantum action variable. Two types of families of states are defined classically and quantum mechanically; radial momentum families and angular momentum families. Phase integral methods are used as one method to find the location of the poles of the quantum momentum function. The Coulomb potential is used as the main example and general methods are described for the other potentials.</p>