The Hellmann potential, which is a superposition of an attractive Coulomb potential −a/r and a Yukawa potential b e−δr/r, is often used to compute bound-state normalizations and energy levels of neutral atoms. By using the generalized parametric Nikiforov—Uvarov (NU) method, we have obtained the approximate analytical solutions of the radial Schrödinger equation (SE) for the Hellmann potential. The energy eigenvalues and corresponding eigenfunctions are calculated in closed forms. Some numerical results are presented, which show good agreement with a numerical amplitude phase method and also those previously obtained by other methods. As a particular case, we find the energy levels of the pure Coulomb potential.

We obtain the bound-state solutions of the radial Schrödinger equation (SE) with the shifted Deng-Fan (sDF) oscillator potential in the frame of the Nikiforov-Uvarov (NU) method and employing Pekeris-type approximation to deal with the centrifugal term. The analytical expressions for the energy eigenvalues and the corresponding wave functions are obtained in closed form for arbitrary l -state. The ro-vibrational energy levels for a few diatomic molecules are also calculated. They are found to be in good agreement with those ones previously obtained by the Morse potential.

A description of scalar waves scattered off a Schwarzschild black hole is discussed in terms of complex angular momenta. In the new picture the scattering amplitude is split into a supposedly smooth background integral and a sum over the so-called Regge poles. It is proved that all the relevant Regge poles (the singularities of the S-matrix) must be situated in the first quadrant of the complex -plane. We also show that the S-matrix possesses a global symmetry relation , which makes it possible to simplify considerably the background integral. Finally, a formal basis for actual computations of Regge poles and the associated residues is outlined.

The Yukawa potential is often used to compute bound-state normalizations and energy levels of neutral atoms. By using the generalized parametric Nikiforov-Uvarov method, we obtain approximate analytical solutions of the radial Schrödinger equation for the Yukawa potential. The energy eigenvalues and the corresponding eigenfunctions are calculated in closed forms. Some numerical results are presented and show that these results are in good agreement with those obtained previously by other methods. Also, we find the energy levels of the familiar pure Coulomb potential energy levels when the screening parameter of the Yukawa potential goes to zero.

The Tietz‐Hua (TH) potential is one of the very best analytical model potentials for the vibrational energy of diatomic molecules. By using the Nikiforov‐Uvarov method, we have obtained the exact analytical s‐wave solutions of the radial Schrödinger equation for the TH potential. The energy eigenvalues and the corresponding eigenfunctions are calculated in closed forms. Some numerical results for diatomic molecules are also presented. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011

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Approaches inspired by a recent amplitude-phase method for analyzing the radial Dirac equation are presented to calculate phase shifts. Regarding the spin- and pseudo-spin symmetries of relativistic spectra, the coupled first-order and the decoupled second-order differential forms of the radial Dirac equation are investigated by using a novel and the ‘classical’ amplitude-phase methods, respectively. The quasi non-relativistic limit of the amplitude-phase formulae is discussed for both positive and negative energies. In the positive (E> mc2) low-energy region, the relativistic effects of scattering phase shifts are discussed based on two scattering potential models. Results are compared with those of non-relativistic calculations. In particular, the numerical results obtained from a rational approximation of the Thomas–Fermi potential are discussed in some detail.