UNEXPECTED PROPERTIES OF THE MORSE OSCILLATOR
Publisher:
Ohio State UniversityAbstract:
Analytical solutions for the Morse oscillator are used to evaluate $\langle V\rangle_n$ and $\langle T\rangle_n$. For all bound states $\langle V\rangle_n= \frac{\hbar \omega_e}{2}\left (n+\frac{1}{2}\right )$. This result is identical to the result that is obtained for the harmonic oscillator with the same quadratic force constant. Consequently, all of the anharmonicity in the energy of the quantum states of a Morse oscillator is incorporated in $\langle T\rangle_n$. This finding is tested for realistic diatomic potential functions for Ar-Xe, $\chem Be_2$ and the $E-$state of $\chem Li_2$. Analysis of $\langle V\rangle_n/\left (n+\frac{1}{2}\right )$ for these systems shows that this quantity is well approximated by $\omega_e/2$ over large ranges of $n$. Implications of this result to polyatomic systems and for vibration to translation collisional energy transfer are discussed., {\bf 501}, 603-607 (2011).} \vspace{3 mm}
Description:
Author Institution: Department of Chemistry, The Ohio State University, Columbus, OH 43210
Type:
ArticleOther Identifiers:
2011-TJ-02Items in Knowledge Bank are protected by copyright, with all rights reserved, unless otherwise indicated.