Polynomial solution of non-central potentials

Ikhdair, Sameer M.
Sever, Ramazan
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.


Exact polynomial solution of PT-/non-PT-symmetric and non-Hermitian modified Woods-Saxon potential by the Nikiforov-Uvarov method
Ikhdair, Sameer M.; Sever, Ramazan (Springer Science and Business Media LLC, 2007-06-01)
UUsing the Nikiforov-Uvarov ( NU) method, the bound state energy eigenvalues and eigenfunctions of the PT-/non-PT-symmetric and non-Hermitian modified Woods-Saxon (WS) model potential with the real and complex-valued energy levels are obtained in terms of the Jacobi polynomials. According to the PT-symmetric quantum mechanics, we exactly solved the time-independent Schrodinger equation with same potential for the s-states and also for any l-state as well. It is shown that the results are in good agreement w...
Analytical solution of the Schrodinger equation for Makarov potential with any l angular momentum
Bayrak, O.; Karakoc, M.; Boztosun, I.; Sever, Ramazan (Springer Science and Business Media LLC, 2008-11-01)
We present the analytical solution of the Schrodinger Equation for the Makarov potential within the framework of the asymptotic iteration method for any n and l quantum numbers. Energy eigenvalues and the corresponding wave functions are calculated. We also obtain the same results for the ring shaped Hartmann potential which is the special form of the non-central Makarov potential.
Time Dependence of Joint Entropy of Oscillating Quantum Systems
ÖZCAN, ÖZGÜR; Akturk, Ethem; Sever, Ramazan (Springer Science and Business Media LLC, 2008-12-01)
The time dependent entropy (or Leipnik's entropy) of harmonic and damped harmonic oscillator systems is studied by using time dependent wave function obtained by the Feynman path integral method. The Leipnik entropy and its envelope change as a function of time, angular frequency and damping factor. Our results for simple harmonic oscillator are in agreement with the literature. However, the joint entropy of damped harmonic oscillator shows remarkable discontinuity with time for certain values of damping fa...
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.
Bound State Solutions of Schrodinger Equation for Generalized Morse Potential with Position-Dependent Mass
Arda, Altug; Sever, Ramazan (IOP Publishing, 2011-07-15)
The effective mass one-dimensional Schrodinger equation for the generalized Morse potential is solved by using Nikiforov-Uvarov method. Energy eigenvalues and corresponding eigenfunctions are computed analytically. The results are also reduced to the constant mass case. Energy eigenvalues are computed numerically for some diatomic molecules. They are in agreement with the ones obtained before.
Citation Formats
S. M. Ikhdair and R. Sever, “Polynomial solution of non-central potentials,” INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS, pp. 2384–2395, 2007, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/62492.