Relativistic and nonrelativistic bound states of the isotonic oscillator by Nikiforov-Uvarov method

Sever, Ramazan
A nonpolynomial one-dimensional quantum potential in the form of an isotonic oscillator (harmonic oscillator with a centripetal barrier) is studied. We provide the nonrelativistic bound state energy spectrum E(n) and the wave functions psi(n)(chi) in terms of the associated Laguerre polynomials in the framework of the Nikiforov-Uvarov method. Under the spin and pseudospin symmetric limits, the analytic eigenvalues and the corresponding two-component upper-and lower-spinors of the Dirac particle are obtained in closed form. (C) 2011 American Institute of Physics. [doi:10.1063/1.3671640]


Approximate Pseudospin and Spin Solutions of the Dirac Equation for a Class of Exponential Potentials
Arda, Altug; Sever, Ramazan; TEZCAN, CEVDET (2010-02-01)
The Dirac equation is solved for some exponential potentials the hypergeometric-type potential, the generalized Morse potential, and the Poschl-Teller potential with any spin-orbit quantum number kappa in the case of spin and pseudospin symmetry. We have approximated for non s-waves the centrifugal term by an exponential form. The energy eigenvalue equations and the corresponding wave functions are obtained by using a generalization of the Nikiforov-Uvarov method.
Relativistic Two-Dimensional Harmonic Oscillator Plus Cornell Potentials in External Magnetic and AB Fields
Ikhdair, Sameer M.; Sever, Ramazan (Hindawi Limited, 2013)
<jats:p>The Klein-Gordon (KG) equation for the two-dimensional scalar-vector harmonic oscillator plus Cornell potentials in the presence of external magnetic and Aharonov-Bohm (AB) flux fields is solved using the wave function ansatz method. The exact energy eigenvalues and the wave functions are obtained in terms of potential parameters, magnetic field strength, AB flux field, and magnetic quantum number. The results obtained by using different Larmor frequencies are compared with the results in the absenc...
Extended dynamical symmetries of Landau levels in higher dimensions
Kürkcüoğlu, Seçkin; YURDUŞEN, İSMET (Springer Science and Business Media LLC, 2020-02-14)
Continuum models for time-reversal (TR) invariant topological insulators (Tis) in d >= 3 dimensions are provided by harmonic oscillators coupled to certain SO(d) gauge fields. These models are equivalent to the presence of spin-orbit (SO) interaction in the oscillator Hamiltonians at a critical coupling strength (equivalent to the harmonic oscillator frequency) and leads to flat Landau Level (LL) spectra and therefore to infinite degeneracy of either the positive or the negative helicity states depending on...
Exact solution of the time-dependent harmonic plus an inverse harmonic potential with a time-dependent electromagnetic field
Yuce, C (2003-12-01)
In this paper, the problem of the charged harmonic plus an inverse harmonic oscillator with time-dependent mass and frequency in a time-dependent electromagnetic field is investigated. It is reduced to the problem of the inverse harmonic oscillator with time-independent parameters and the exact wave function is obtained.
Streamwise oscillations of a cylinder beneath a free surface: Free surface effects on vortex formation modes
Bozkaya, Canan; Mironova, L. A.; Gubanov, O. I. (Elsevier BV, 2011-06-15)
A computational study of a viscous incompressible two-fluid model with an oscillating cylinder is investigated at a Reynolds number of 200 and at a dimensionless displacement amplitude of A = 0.13 and for the dimensionless forcing cylinder oscillation frequency-to-natural vortex shedding frequency ratios, f/f(0) = 1.5, 2.5, 3.5. Specifically, two-dimensional flow past a circular cylinder subject to forced in-line oscillations beneath a free surface is considered. The method is based on a finite volume discr...
Citation Formats
S. IKHDAİR and R. Sever, “Relativistic and nonrelativistic bound states of the isotonic oscillator by Nikiforov-Uvarov method,” JOURNAL OF MATHEMATICAL PHYSICS, pp. 0–0, 2011, Accessed: 00, 2020. [Online]. Available: