Bohr Sommerfeld quantisation and molecular potentials View Full Text


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Article Info

DATE

2011-10-18

AUTHORS

Shayak Bhattacharjee, D. S. Ray, J. K. Bhattacharjee

ABSTRACT

We combine, within the Bohr Sommerfeld quantization rule, a systematic perturbation with asymptotic analysis of the action integral for potentials which support a finite number of bound states with E < 0 to obtain an interpolation formula for the energy eigenvalues. We find interpolation formulae for the Morse potential as well as potentials of the form \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${V=V_0 \left[ {\left( {\frac{a}{x}} \right)^{2k}-\left( {\frac{a}{x}}\right)^{k}} \right]}$$\end{document}. For k = 6 i.e. the well known Lennard Jones potential this yields results within 1 per cent of the highly accurate numerical values. For the Morse potential this procedure yields the exact answer. We find that the result for the Morse potential which approaches zero exponentially is the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${k\rightarrow\infty}$$\end{document} limit of the Lennard Jones class of potentials. More... »

PAGES

819-832

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s10910-011-9926-0

DOI

http://dx.doi.org/10.1007/s10910-011-9926-0

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1031378699


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