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International Journal of the Physical Sciences

The Dirac equation with position-dependent mass for the modified Pschl-Teller potential and its solution

Yasuk, Bahar

Published Nov 30, 2012• 0 citations
Publisher

Abstract

The Dirac-modified Poschl-Teller problem with position dependent mass is investigated within the framework of the asymptotic iteration method in N dimensions. Any -state solutions are obtained by using the exponential approximation for the centrifugal term. The energy eigenvalues and two-component spinor corresponding eigenfunctions are determined for different  screening parameters explicitly. The corresponding eigenfunctions obtained in the form of hypergeometric functions are normalized and plotted for different quantum states. Effects on modified Poschl-Teller potential, bound state energy eigenvalues and normalized corresponding eigenfunctions of the  screening parameters are investigated and its results are discussed.    Key words: Dirac equation, position-dependent mass (PDM), Poschl-Teller (PT) potential, asymptotic iteration method, bound state.

DOI
10.5897/ijps12.628

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Physica Scripta•Nov 21, 2013•8 citations
The Dirac-modified Poschl-Teller problem with position dependent mass is investigated within the framework of the asymptotic iteration method in N dimensions. Any -state solutions are obtained by using the exponential approximation for the centrifugal term. The energy eigenvalues and two-component spinor corresponding eigenfunctions are determined for different  screening parameters explicitly. The corresponding eigenfunctions obtained in the form of hypergeometric functions are normalized and plotted for different quantum states. Effects on modified Poschl-Teller potential, bound state energy eigenvalues and normalized corresponding eigenfunctions of the  screening parameters are investigated and its results are discussed. 
 

Key words: Dirac equation, position-dependent mass (PDM), Poschl-Teller (PT) potential, asymptotic iteration method, bound state.
By employing an exponential-type approximation scheme to replace the centrifugal term, we have approximately solved the Dirac equation for a spin-1/2 particle subjected to complex parity–time-symmetric scalar and vector Pöschl–Teller (PT) potentials with arbitrary spin–orbit -wave states in view of spin and pseudospin (p-spin) symmetries. The real bound-state energy eigenvalue equation and the corresponding two-spinor components wave function expressible in terms of hypergeometric functions are obtained by means of wave function analysis. The spin- Dirac equation and the spin-0 Klein–Gordon equation with complex PT potentials share the same energy spectrum under the choice of (i.e. exact spin and p-spin symmetries).
We study the Dirac equation with position dependent mass (PDM) for Modified Manning Rosen potential. The Dirac equation with PDM is solved using Laplace method to obtain the energy equation and the wave function. We calculate the energy eigenvalues and the wave function numerically for several quantum numbers and parameters potential. The results showed that the energy eigenvalue increases as the quantum number and the parameters potential increase. The variation of the parameter potential gives the different of waveforms in each state.
Approximate κ\kappaκ -state solutions of the Dirac equation in spatially dependent mass for the Eckart potential including the Yukawa tensor interaction
We investigate the analytical approximation to arbitrary -state solutions of the Dirac equation with the position-dependent mass particle in the Eckart potential including the Yukawa tensor interaction in the framework of a parametric Nikiforov–Uvarov method. By taking a proper approximation to deal with the centrifugal term, the analytical relativistic energy eigenvalues and the corresponding normalized two-spinor components of the wave function are obtained in closed form. The relativistic and non-relativistic bound state solutions for some special cases, such as the Hulthén potential and the generalized Morse potential, are easily obtained from our general solution.