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arXiv · 0909.1218

Approximate analytic solutions of the diatomic molecules in the Schrodinger equation with hyperbolical potentials

Sameer M. Ikhdair·Ramazan Sever
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Abstract

The Schrodinger equation for the rotational-vibrational (ro-vibrational) motion of a diatomic molecule with empirical potential functions is solved approximately by means of the Nikiforov-Uvarov method. The approximate ro-vibratinal energy spectra and the corresponding normalized total wavefunctions are calculated in closed form and expressed in terms of the hypergeometric functions or Jacobi polynomials P_{n}^{(μ,ν)}(x), where μ>-1, ν>-1 and x included in [-1,+1]. The s-waves analytic solution is obtained. The numerical energy eigenvalues for selected H_{2} and Ar_{2} molecules are also calculated and compared with the previous models and experiments.

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Sameer M. Ikhdair, Ramazan Sever. 2009-09-07. Approximate analytic solutions of the diatomic molecules in the Schrodinger equation with hyperbolical potentials. https://doi.org/10.1002/andp.200910369

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