%0 Journal Article %1 mikulski2014approximate %A Mikulski, Damian %A Eder, Krzysztof %A Konarski, Jerzy %D 2014 %I Springer International Publishing %J Journal of Mathematical Chemistry %K equation mechanics physics quantum schrodinger solution unread %N 5 %P 1364-1371 %R 10.1007/s10910-014-0316-2 %T Approximate analytical solutions of the stationary radial Schrödinger equation with new anharmonic potentials %U http://dx.doi.org/10.1007/s10910-014-0316-2 %V 52 %X For a high accuracy description of bond-stretching vibrations of diatomic molecules new analytic five and six-parameter potential energy functions have been proposed. These potentials include parameters that can be determined with the use of a direct fit to measured energy level spacings. The corresponding stationary radial Schrödinger equations with these potential energy functions are solved analytically, in an approximate scheme for zero total angular momentum. It is found that the wave functions for bound states can be expressed in terms of the Jacoby polynomial. The analytical expressions for purely vibrational energy levels have been derived within the algebraic approach. The potentials presented can be very useful for theoretical spectroscopic studies to reproduce the vibrational spectra of diatomic molecules.

@article{mikulski2014approximate, abstract = {For a high accuracy description of bond-stretching vibrations of diatomic molecules new analytic five and six-parameter potential energy functions have been proposed. These potentials include parameters that can be determined with the use of a direct fit to measured energy level spacings. The corresponding stationary radial Schrödinger equations with these potential energy functions are solved analytically, in an approximate scheme for zero total angular momentum. It is found that the wave functions for bound states can be expressed in terms of the Jacoby polynomial. The analytical expressions for purely vibrational energy levels have been derived within the algebraic approach. The potentials presented can be very useful for theoretical spectroscopic studies to reproduce the vibrational spectra of diatomic molecules.}, added-at = {2014-04-03T22:56:42.000+0200}, author = {Mikulski, Damian and Eder, Krzysztof and Konarski, Jerzy}, biburl = {https://www.bibsonomy.org/bibtex/2be0147de7758e4000eed0826bf0959d5/drmatusek}, doi = {10.1007/s10910-014-0316-2}, interhash = {6950792812ecb0d8491fb57604034c26}, intrahash = {be0147de7758e4000eed0826bf0959d5}, issn = {0259-9791}, journal = {Journal of Mathematical Chemistry}, keywords = {equation mechanics physics quantum schrodinger solution unread}, language = {English}, month = may, number = 5, pages = {1364-1371}, publisher = {Springer International Publishing}, timestamp = {2014-04-03T22:56:42.000+0200}, title = {Approximate analytical solutions of the stationary radial Schrödinger equation with new anharmonic potentials}, url = {http://dx.doi.org/10.1007/s10910-014-0316-2}, volume = 52, year = 2014 }