Exponential Type Complex and non-Hermitian Potentials in PT-Symmetric Quantum Mechanics

Using the NU method [A.F.Nikiforov, V.B.Uvarov, Special Functions of Mathematical Physics, Birkhauser,Basel,1988], we investigated the real eigenvalues of the complex and/or $PT$- symmetric, non-Hermitian and the exponential type systems, such as Poschl-Teller and Morse potentials.Comment: 14 pages, Late

An Improvement of the Asymptotic Iteration Method for Exactly Solvable Eigenvalue Problems

We derive a formula that simplifies the original asymptotic iteration method formulation to find the energy eigenvalues for the analytically solvable cases. We then show that there is a connection between the asymptotic iteration and the Nikiforov--Uvarov methods, which both solve the second order linear ordinary differential equations analytically.Comment: RevTex4, 8 page

A General Approach for the Exact Solution of the Schrodinger Equation

The Schr\"{o}dinger equation is solved exactly for some well known potentials. Solutions are obtained reducing the Schr\"{o}dinger equation into a second order differential equation by using an appropriate coordinate transformation. The Nikiforov-Uvarov method is used in the calculations to get energy eigenvalues and the corresponding wave functions.Comment: 20 page

Classical Simulation of Relativistic Quantum Mechanics in Periodic Optical Structures

Spatial and/or temporal propagation of light waves in periodic optical structures offers a rather unique possibility to realize in a purely classical setting the optical analogues of a wide variety of quantum phenomena rooted in relativistic wave equations. In this work a brief overview of a few optical analogues of relativistic quantum phenomena, based on either spatial light transport in engineered photonic lattices or on temporal pulse propagation in Bragg grating structures, is presented. Examples include spatial and temporal photonic analogues of the Zitterbewegung of a relativistic electron, Klein tunneling, vacuum decay and pair-production, the Dirac oscillator, the relativistic Kronig-Penney model, and optical realizations of non-Hermitian extensions of relativistic wave equations.Comment: review article (invited), 14 pages, 7 figures, 105 reference

The Klein-Gordon equation of generalized Hulthen potential in complex quantum mechanics

WOS: 000221420200011We have investigated the reality of exact bound states of complex and/or PT-symmetric non-Hermitian exponential-type, generalized Hulthen potential. The Klein-Gordon equation has been solved by using the Nikiforov-Uvarov method which is based on solving the second-order linear differential equations by reduction to a generalized equation of hypergeometric type. In many cases of interest, negative and positive energy states have been discussed for different types of complex potentials

Bound-state solutions of the Klein-Gordon equation for the generalized PT-symmetric Hulthén potential

The one-dimensional Klein-Gordon equation is solved for the PT-symmetric generalized Hulthén potential in the scalar coupling scheme. The relativistic bound-state energy spectrum and the corresponding wave functions are obtained by using the Nikiforov-Uvarov method which is based on solving the second-order linear differential equations by reduction to a generalized equation of hypergeometric type. © Springer Science+Business Media, LLC 2007

Exact solutions of the Schrodinger equation for the deformed hyperbolic potential well and the deformed four-parameter exponential type potential

WOS: 000089961900001Exact solutions of the Schrodinger equation for two 'deformed hyperbolic potentials' that were introduced by Arai [J. Math. Anal. Appl. 158 (1991) 63] have been obtained by using an analytical solution method which has been developed by Nikiforov and Uvarov [Special Functions of Mathematical Physics, Birkhauser, Basel, 1988] for the solutions of the differential equations of hypergeometric type in which the solutions are special functions. (C) 2000 Published by Elsevier Science B.V