RENORMALIZED PERTURBATION-SERIES AND THE SEMICLASSICAL LIMIT OF QUANTUM-MECHANICS

The accuracy of the renormalized perturbation series for anharmonic oscillators and other simple quantum-mechanical models increases with the quantum number when the adjustable parameter is determined by a simple variational criterion. In the semiclassical limit of quantum mechanics such an expansion converges towards the result of the Jeffreys-Wentzel-Kramers-Brillouin method to all orders. The hypervirial and Hellmann-Feynman theorems facilitate the derivation of the semiclassical series from Rayleigh-Schrodinger perturbation theory. (C) 1995 American Institute of Physics.