An approximate solution of the Schrödinger equation with the Hulthén potential is obtained in D-dimensions with an exponential approximation of the centrifugal term. Solution to the corresponding hyperradial equation is given using the conventional Nikiforov-Uvarov method. The normalization constants for the Hulthén potential are also computed. The expectation values r −2 , V (r) , are also obtained using the FeynmanHellmann theorem.

Abtract:We present the solutions of the Schrödinger equation with the Hulthén potential plus ring-shape potential for ℓ = 0 states within the framework of an exponential approximation of the centrifugal potential. Solutions to the corresponding angular and radial equations are obtained in terms of special functions using the conventional Nikiforov-Uvarov method. The normalization constant for the Hulthén potential is also computed.

We present new quasi-exactly solvable models with inverse quartic, sextic, octic and decatic power potentials, respectively. We solve these models exactly via the functional Bethe ansatz method. For each case, we give closed-form solutions for the energies and the wave functions as well as analytical expressions for the allowed potential parameters in terms of a set of algebraic equations.Comment: LaTex 18 pages. Updated version to appear in Annals of Physic

An approximate solution of the D-dimensional Schrödinger equation with the modified Pöschl-Teller potential is obtained with an approximation of the centrifugal term. Solution to the corresponding hyper-radial equation is given using the conventional Nikiforov-Uvarov method. The normalization constants for the Pöschl-Teller potential are also computed. The expectation values r −2 , V (r) , are also obtained using the Feynman-Hellmann theorem.

We present solutions of the Dirac equation with spin symmetry for vector and scalar modified Pöschl-Teller potentials within the framework of an approximation of the centrifugal term. The relativistic energy spectrum is obtained using the Nikiforov-Uvarov method and the two-component spinor wave functions obtained are in terms of the Jacobi polynomials. It is found that there exist only positive energy states for bound states under spin symmetry, and the energy of a level with fixed value of n, increases with increase in dimension of space time and the potential range parameter α.