Bohr Sommerfeld quantisation and molecular potentials
Mathematical Physics
2011-12-20 v1 math.MP
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.
Cite
@article{arxiv.1112.4247,
title = {Bohr Sommerfeld quantisation and molecular potentials},
author = {Shayak Bhattacharjee and D. S. Ray and J. K. Bhattacharjee},
journal= {arXiv preprint arXiv:1112.4247},
year = {2011}
}
Comments
Use of perturbation theory and Bohr Sommerfeld quantisation to find energy eigenvalues of some potentials; Journal of Mathematical Chemistry online first Oct. 18, 2011