A search on the Nikiforov-Uvarov formalism

An alternative treatment is proposed for the calculations carried out within the frame of Nikiforov-Uvarov method, which removes a drawback in the original theory and by pass some difficulties in solving the Schrodinger equation. The present procedure is illustrated with the example of orthogonal polynomials. The relativistic extension of the formalism is discussed.Comment: 10 page

A search on Dirac equation

The solutions, in terms of orthogonal polynomials, of Dirac equation with analytically solvable potentials are investigated within a novel formalism by transforming the relativistic equation into a Schrodinger like one. Earlier results are discussed in a unified framework and certain solutions of a large class of potentials are given.Comment: 9 page

Supersymmetric approach to exactly solvable systems with position-dependent effective masses

We discuss the relationship between exact solvability of the Schr\"{o}dinger equation with a position-dependent mass and the ordering ambiguity in the Hamiltonian operator within the frame of supersymmetric quantum mechanics. The one-dimensional Schr\"{o}dinger equation, derived from the general form of the effective mass Hamiltonian, is solved exactly for a system with exponentially changing mass in the presence of a potential with similar behaviour, and the corresponding supersymmetric partner Hamiltonians are related to the effective-mass Hamiltonians proposed in the literature.Comment: 12 pages article in LaTEX (uses standard article.sty). Please check http://www1.gantep.edu.tr/~ozer for other studies of Nuclear Physics Group at University of Gaziantep. [arXiv admin note: excessive overlap with quant-ph/0306065 and "Supersymmetric approach to quantum systems with position-dependent effective mass" by A. R. Plastino, A. Rigo, M. Casas, F. Garcias, and A. Plastino - Phys. Rev. A 60, 4318 - 4325 (1999)

A note on the Woods-Saxon potential

The wave Schrodinger and, to clarify one interesting point encountered in the calculations, Klein-Gordon equations are solved exactly for a single neutron moving in a central Woods-Saxon plus an additional potential that provides a flexibility to construct the surface structure of the related nucleus. The physics behind the solutions and the reliability of the results obtained are discussed carefully with the consideration of other related works in the literature. In addition, the exhaustive analysis of the results reveals the fact that the usual Woods-Saxon potential cannot be solved analytically within the framework of non-relativistic physics, unlike its exactly solvable relativistic consideration

Pseudo-Hermitian versus Hermitian position-dependent-mass Hamiltonians in a perturbative framework

We formulate a systematic algorithm for constructing a whole class of Hermitian position-dependent-mass Hamiltonians which, to lowest order of perturbation theory, allow a description in terms of PT-symmetric Hamiltonians. The method is applied to the Hermitian analogue of the PT-symmetric cubic anharmonic oscillator. A new example is provided by a Hamiltonian (approximately) equivalent to a PT-symmetric extension of the one-parameter trigonometric Poschl-Teller potential.Comment: 13 pages, no figure, modified presentation, 6 additional references, published versio

A general scheme for the effective-mass Schrodinger equation and the generation of the associated potentials

A systematic procedure to study one-dimensional Schr\"odinger equation with a position-dependent effective mass (PDEM) in the kinetic energy operator is explored. The conventional free-particle problem reveals a new and interesting situation in that, in the presence of a mass background, formation of bound states is signalled. We also discuss coordinate-transformed, constant-mass Schr\"odinger equation, its matching with the PDEM form and the consequent decoupling of the ambiguity parameters. This provides a unified approach to many exact results known in the literature, as well as to a lot of new ones.Comment: 16 pages + 1 figure; minor changes + new "free-particle" problem; version published in Mod. Phys. Lett.

Spectrum generating algebras for position-dependent mass oscillator Schrodinger equations

The interest of quadratic algebras for position-dependent mass Schr\"odinger equations is highlighted by constructing spectrum generating algebras for a class of d-dimensional radial harmonic oscillators with $d \ge 2$ and a specific mass choice depending on some positive parameter $\alpha$. Via some minor changes, the one-dimensional oscillator on the line with the same kind of mass is included in this class. The existence of a single unitary irreducible representation belonging to the positive-discrete series type for $d \ge 2$ and of two of them for d=1 is proved. The transition to the constant-mass limit $\alpha \to 0$ is studied and deformed su(1,1) generators are constructed. These operators are finally used to generate all the bound-state wavefunctions by an algebraic procedure.Comment: 21 pages, no figure, 2 misprints corrected; published versio

PT-symmetric Solutions of Schrodinger Equation with position-dependent mass via Point Canonical Transformation

PT-symmetric solutions of Schrodinger equation are obtained for the Scarf and generalized harmonic oscillator potentials with the position-dependent mass. A general point canonical transformation is applied by using a free parameter. Three different forms of mass distributions are used. A set of the energy eigenvalues of the bound states and corresponding wave functions for target potentials are obtained as a function of the free parameter.Comment: 13 page

Polynomial Solution of Non-Central Potentials

We show that the exact energy eigenvalues and eigenfunctions of the Schrodinger equation for charged particles moving in certain class of non-central potentials can be easily calculated analytically in a simple and elegant manner by using Nikiforov and Uvarov (NU) method. We discuss the generalized Coulomb and harmonic oscillator systems. We study the Hartmann Coulomb and the ring-shaped and compound Coulomb plus Aharanov-Bohm potentials as special cases. The results are in exact agreement with other methods.Comment: 18 page

Approximate solution of the Duffin-Kemmer-Petiau equation for a vector Yukawa potential with arbitrary total angular momenta

The usual approximation scheme is used to study the solution of the Duffin-Kemmer-Petiau (DKP) equation for a vector Yukawa potential in the framework of the parametric Nikiforov-Uvarov (NU) method. The approximate energy eigenvalue equation and the corresponding wave function spinor components are calculated for arbitrary total angular momentum in closed form. Further, the approximate energy equation and wave function spinor components are also given for case. A set of parameter values is used to obtain the numerical values for the energy states with various values of quantum levelsComment: 17 pages; Communications in Theoretical Physics (2012). arXiv admin note: substantial text overlap with arXiv:1205.0938, and with arXiv:quant-ph/0410159 by other author