Improved analytical approximation to arbitrary l-state solutions of the Schrodinger equation for the hyperbolical potentials

Sever, Ramazan
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 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 is an element of[-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. (C) 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim


Approximate solution to the time-dependent Kratzer plus screened Coulomb potential in the Feinberg-Horodecki equation
Farout, Mahmoud; Sever, Ramazan; Ikhdair, Sameer M. (IOP Publishing, 2020-06-01)
We obtain the quantized momentum eigenvalues P-n together with space-like coherent eigenstates for the space-like counterpart of the Schrodinger equation, the Feinberg-Horodecki equation, with a combined Kratzer potential plus screened coulomb potential which is constructed by temporal counterpart of the spatial form of these potentials. The present work is illustrated with two special cases of the general form: the time-dependent modified Kratzer potential and the time-dependent screened Coulomb potential.
Approximate analytical solutions of the pseudospin symmetric Dirac equation for exponential-type potentials
Arda, Altu; Sever, Ramazan; TEZCAN, CEVDET (Wiley, 2009-10-01)
The solvability of The Dirac equation is studied for the exponential-type potentials with the pseudospin symmetry by using the parametric generalization of the Nikiforov-Uvarov method. The energy eigenvalue equation, and the corresponding Dirac spinors for Morse, Hulthen, and q-deformed Rosen-Morse potentials are obtained within the framework of an approximation to the spin-orbit coupling term, so the solutions are given for any value of the spin-orbit quantum number kappa = 0, or kappa not equal 0. (C) 200...
Exact solution of the Dirac equation with the Mie-type potential under the pseudospin and spin symmetry limit
Aydogdu, Oktay; Sever, Ramazan (Elsevier BV, 2010-02-01)
We investigate the exact solution of the Dirac equation for the Mie-type potentials under the conditions of pseudospin and spin symmetry limits. The bound state energy equations and the corresponding two-component spinor wave functions of the Dirac particles for the Mie-type potentials with pseudospin and spin symmetry are obtained. We use the asymptotic iteration method in the calculations. Closed forms of the energy eigenvalues are obtained for any spin-orbit coupling term K. We also investigate the energ...
Analytical Solutions to the Klein-Gordon Equation with Position-Dependent Mass for q-Parameter Poschl-Teller Potential
Arda, Altug; Sever, Ramazan; TEZCAN, CEVDET (IOP Publishing, 2010-01-01)
The energy eigenvalues and the corresponding eigenfunctions of the one-dimensional Klein-Gordon equation with q-parameter Poschl-Teller potential are analytically obtained within the position-dependent mass formalism. The parametric generalization of the Nikiforov-Uvarov method is used in the calculations by choosing a mass distribution.
Effective polar potential in the central force Schrodinger equation
Shikakhwa, M. S.; Mustafa, M. (IOP Publishing, 2010-01-01)
The angular part of the Schrodinger equation for a central potential is brought to the one-dimensional 'Schrodinger form' where one has a kinetic energy plus potential energy terms. The resulting polar potential is seen to be a family of potentials characterized by the square of the magnetic quantum number m. It is demonstrated that this potential can be viewed as a confining potential that attempts to confine the particle to the xy-plane, with a strength that increases with increasing m. Linking the soluti...
Citation Formats
S. IKHDAİR and R. Sever, “Improved analytical approximation to arbitrary l-state solutions of the Schrodinger equation for the hyperbolical potentials,” ANNALEN DER PHYSIK, pp. 747–758, 2009, Accessed: 00, 2020. [Online]. Available: