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

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

2009-09-07

arxiv.org/abs/0909.1218v1

Ann. Phys. 18 (10-11) (2009) 747-758.

Physics

Quantum Physics

18 pages

Scientific paper

10.1002/andp.200910369

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}^{(\mu,\nu)}(x), where \mu>-1, \nu>-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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