Approximate analytic solutions of the diatomic molecules in the Schrodinger equation with hyperbolical potentials
arXiv:0909.1218 · doi:10.1002/andp.200910369
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
References in corpus (6)
- An improved approximation scheme for the centrifugal term and the Hulthen potential
- Exact Klein-Gordon equation with spatially-dependent masses for unequal scalar-vector Coulomb-like potentials
- Exact Solution of the Klein-Gordon Equation for the PT-Symmetric Generalized Woods-Saxon Potential by the Nikiforov-Uvarov Method
- Any l-state improved quasi-exact analytical solutions of the spatially dependent mass Klein-Gordon equation for the scalar and vector Hulthen potentials
- Approximate l-state solutions of the D-dimensional Schrodinger equation for Manning-Rosen potential
- Bound states of the Klein-Gordon equation for vector and scalar general Hulthen-type potentials in D-dimension