Comment on "The Rotation-Vibration Spectrum of Diatomic Molecules with the Tietz-Hua Rotating Oscillator"

Abstract

We present arguments demonstrating that the application of the Nikiforov-Uvarov polynomial method to solve the Schrödinger equation with the Tietz-Hua potential is valid only when $e^{-b_h{r}_e}\le c_h<1$ and $r_0<r<+\infty$. In particular, it is pointed out that the numerical results with $c_h\ne 0$ for the diatomic molecules $\mathrm{HF}$, ${\mathrm{N}}_2$, ${\mathrm{I}}_2$, ${\mathrm{H}}_2$, ${\mathrm{O}}_2$ and ${\mathrm{O}}_2^{+}$ given in Tables 3-5 by Hamzavi and co-workers are wrong. When $-1\le c_h<0$ or $0<c_h<e^{-b_h{r}_e}$, this approach is not suitable. In both cases, it is shown that the solutions of the Schrödinger equation are expressed in terms of the generalized hypergeometric functions ${}_2{F}_1\left(a,b,c;z\right)$. The determination of the energy levels requires the solution of transcendantal equations involving the hypergeometric function by means of the numerical procedure.

arXiv comment7 pages, no figures

References in corpus (1)

• The Rotation-Vibration Spectrum of Diatomic Molecules with the Tietz-Hua Rotating oscillator