Bohr Sommerfeld quantisation and molecular potentials

TL;DR

This paper applies Bohr Sommerfeld quantization with perturbation theory to accurately compute energy levels for various molecular potentials, confirming the method's effectiveness and providing precise results.

Contribution

It introduces a combined perturbative and asymptotic approach to find exact and highly accurate energy levels for several molecular potentials.

Findings

Exact energy levels for P"oschl-Teller, Morse, and Rosen Morse potentials.

Over 0.1% accuracy in Lennard-Jones potential energy levels.

Confirmation that perturbation results for certain potentials are exact.

Abstract

We use the Bohr Sommerfeld quantization rule along with a perturbative evaluation of the action intergral to find exact energy levels for the P\"oschl-Teller potential (both hyperbolic and trigonometric forms), the Morse potential, and the Rosen Morse potential. Combining perturbation theory with the simplest asymptotic evaluation of the action integral allows us to obtain all the energy levels of the Lennard-Jones potential with an accuracy greater than 0.1 per cent and serves to confirm that the perturbation results for P\"oschl-Teller and Morse Potentials are exact.