Semiclassical Treatment of High-Lying Electronic States of H${}_2^{+}$

Abstract

This work reports quantum mechanical and semiclassical WKB calculations for energies and wave functions of high-lying ${}^2\Sigma$ states of H${}_2^{+}$ in atomic units. The high-lying states presented lie in an unexplored regime, corresponding asymptotically to H $(n\le 145)$ plus a proton, with $R\le 120,000$ $a_0$. We compare quantum mechanical energies, spectroscopic constants, dipole matrix elements, and phases with semiclassical results and demonstrate a good level of agreement. The quantum mechanical phases are determined by using Milne's phase-amplitude procedure. Our semiclassical energies for low-lying states are compared with those published previously in the literature.

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• Phase-amplitude formalism for ultra-narrow shape resonances
• Generalized spheroidal wave equation for real and complex valued parameters. An algorithm based on the analytic derivatives for the eigenvalues