The Determination of Phases and Amplitudes of Wave Functions

Abstract

The asymptotic forms of the positive energy solutions of the radial Schrödinger equation for a modified Coulomb field are investigated, using both the Jeffreys or WKB method, and the analytic properties of the solutions for an unmodified Coulomb field. The neutral case is also treated. Analytic expressions for the phases associated with modifying potentials of the form αr-2 + βr-3 + γr-4 are obtained, so that the phases and amplitudes of solutions may easily be determined, to sufficient accuracy for most purposes, for any potential of physical interest. A short table of regular and irregular Coulomb functions is given.