The general one-dimensional potential energy function, including centrifugal distortion, for a diatomic molecule is morphed with a series of Morse-like functions for each of the rotational quantum numbers J. For each of the morphed potential, explicit formulae for the matrix elements of the complete energy matrix, on the basis of the solutions of the one-dimensional harmonic oscillator, are given and these may be used in connection with the variational procedure to solve the corresponding vibrational Schrödinger equation. From the set of vibrational levels EvJ,J=0,1,2,… the ro-vibrational transitions can be deduced.
%0 Journal Article
%1 letelier2013variational
%A Letelier, Ricardo D.
%D 2013
%I Springer Netherlands
%J Journal of Mathematical Chemistry
%K equation mechanics physics quantum schrodinger solution spectroscopy
%N 3
%P 1036-1042
%R 10.1007/s10910-012-0135-2
%T On the variational solution of morphed molecular potential in a diatomic molecule
%U http://dx.doi.org/10.1007/s10910-012-0135-2
%V 51
%X The general one-dimensional potential energy function, including centrifugal distortion, for a diatomic molecule is morphed with a series of Morse-like functions for each of the rotational quantum numbers J. For each of the morphed potential, explicit formulae for the matrix elements of the complete energy matrix, on the basis of the solutions of the one-dimensional harmonic oscillator, are given and these may be used in connection with the variational procedure to solve the corresponding vibrational Schrödinger equation. From the set of vibrational levels EvJ,J=0,1,2,… the ro-vibrational transitions can be deduced.
@article{letelier2013variational,
abstract = {The general one-dimensional potential energy function, including centrifugal distortion, for a diatomic molecule is morphed with a series of Morse-like functions for each of the rotational quantum numbers J. For each of the morphed potential, explicit formulae for the matrix elements of the complete energy matrix, on the basis of the solutions of the one-dimensional harmonic oscillator, are given and these may be used in connection with the variational procedure to solve the corresponding vibrational Schrödinger equation. From the set of vibrational levels { EvJ},J=0,1,2,… the ro-vibrational transitions can be deduced.},
added-at = {2013-02-22T15:54:17.000+0100},
author = {Letelier, Ricardo D.},
biburl = {https://www.bibsonomy.org/bibtex/20e5b51cdea632c869e926a6261d6a5d6/drmatusek},
doi = {10.1007/s10910-012-0135-2},
interhash = {38bb20b6de0a097440472594efef8939},
intrahash = {0e5b51cdea632c869e926a6261d6a5d6},
issn = {0259-9791},
journal = {Journal of Mathematical Chemistry},
keywords = {equation mechanics physics quantum schrodinger solution spectroscopy},
language = {English},
month = mar,
number = 3,
pages = {1036-1042},
publisher = {Springer Netherlands},
timestamp = {2014-03-13T21:23:57.000+0100},
title = {On the variational solution of morphed molecular potential in a diatomic molecule},
url = {http://dx.doi.org/10.1007/s10910-012-0135-2},
volume = 51,
year = 2013
}