Özlem Yeşiltaş

PT/non-PT symmetric and non-Hermitian Pöschl–Teller-like solvable potentials via Nikiforov–Uvarov method

The solutions of trigonometric Scarf potential, PT/non-PT symmetric and non-Hermitian q-deformed hyperbolic Scarf and Manning–Rosen potentials are obtained by solving the Schrodinger equation. The Nikiforov–Uvarov method is used to obtain the real energy spectra and corresponding eigenfunctions.

Generalized quantum isotonic nonlinear oscillator in d dimensions

We present a supersymmetric analysis for the d-dimensional Schroedinger equation with the generalized isotonic nonlinear-oscillator potential V(r)={B^2}/{r^{2}}+\omega^{2} r^{2}+2g{(r^{2}-a^{2})}/{(r^{2}+a^{2})^{2}}, B\geq 0. We show that the eigenequation for this potential is exactly solvable provided g=2 and (\omega a^2)^2 = B^2 +(\ell +(d-2)/2)^2. Under these conditions, we obtain explicit formulae for all the energies and normalized bound-state wavefunctions.

Exact solution of Effective mass Schrodinger Equation for the Hulthen potential

A general form of the effective mass Schrödinger equation is solved exactly for Hulthen potential. Nikiforov-Uvarov method is used to obtain energy eigenvalues and the corresponding wave functions. A free parameter is used in the transformation of the wave function.

The quantum effective mass Hamilton–Jacobi problem

In this paper, the quantum Hamilton–Jacobi theory based on the position-dependent mass model is studied. Two effective mass functions having different singularity structures are used to examine the Morse and Poschl–Teller potentials. The residue method is used to obtain the solutions of the quantum effective mass- Hamilton–Jacobi equation. Further, it is shown that the eigenstates of the generalized non-Hermitian Swanson Hamiltonian for Morse and Poschl–Teller potentials can be obtained by using the Riccati equation without solving a differential equation.

Solutions of Three-Dimensional Separable Non-Central Potential

We show that a wide class of non-central potentials can be analysed via the improved picture of the Nikiforov–Uvarov method [Physica Scripta 75 (2007) 686]. It has been shown that using the alternative approach, polynomial solutions of three-dimensional separable non-central potential can be obtained.

Quantum isotonic nonlinear oscillator as a Hermitian counterpart of Swanson Hamiltonian and pseudo-supersymmetry

Within the ideas of pseudo-supersymmetry, we have studied a non-Hermitian Hamiltonian

Comparison theorems for the Dirac equation with spin-symmetric and pseudo-spin-symmetric interactions

H_{-}=\omega(\xi^{\dag} \xi+\1/2)+\alpha \xi^{2}+\beta \xi^{\dag 2}

Supersymmetric analysis of the Dirac-Weyl operator within PT symmetry

, where

Metric operator for the non-Hermitian Hamiltonian model and pseudo-super-symmetry

\alpha \neq \beta

Factorization and Lie point symmetries of general Lienard-type equation in the complex plane

and