Modified method of perturbed stationary states. II. Semiclassical approximation

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Abstract
For one-electron heteropolar systems, a previously derived quantum-mechanical Lagrangian is simplifed using a semiclassical approximation. Unitarity and detailed balancing are retained. The variational method described by Demkov is used to determine the coupled differential equations for the radial scattering functions and the Euler-Lagrange equations for the translational parameters which are part of the theory. Specific semiclassical formulas for the translational parameters are given in a many-state approximation. For a one-state expansion the parameters agree with an earlier determination by Riley and Green.