Semiclassical Treatment of High-Lying Electronic States of H₂ ⁺

We report quantum-mechanical and semiclassical WKB calculations for energies and wave functions of high-lying ²σ states of H₂ ⁺ in atomic units. The high-lying states we present lie in an unexplored regime, corresponding asymptotically to H (n ≤ 146) plus a proton, with R ≤ 120 000a₀. We compare quantum-mechanical energies, spectroscopic constants, dipole matrix elements, and phases with semiclassical results and demonstrate a high level of agreement. Our quantum-mechanical phases were determined by using Milne's phase-amplitude procedure. We compare our semiclassical energies for low-lying states with those of other researchers.