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

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.

18 pages

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Cited by in corpus (6)

• Eigensolution techniques, their applications and the Fisher's information entropy of Tietz-Wei diatomic molecular model
• On the bound-state solutions of the Manning-Rosen potential including improved approximation to the orbital centrifugal term
• Equivalence of the empirical shifted Deng-Fan oscillator potential for diatomic molecules
• Exact Solution of Dirac Equation with Charged Harmonic Oscillator in Electric Field: Bound States
• Approximate bound states of the Dirac equation with some physical quantum potentials
• Studies on the bound-state spectrum of hyperbolic potential