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arXiv:1208.4960 · Physica Scripta

Approximate Dirac solutions of a complex parity–time-symmetric Pöschl–Teller potential in view of spin and pseudospin symmetries

Sameer M Ikhdair, Majid Hamzavi

Published Sep 27, 2012• 14 citations
arXivHTMLPDF

Abstract

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).

DOI
10.1088/0031-8949/86/04/045002

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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).
An approximate solution of the Dirac equation for a spin-1/2 particle under the influence of q -deformed hyperbolic Pöschl–Teller potential combined with trigonometric Scarf II non-central potential is studied analytically. It is assumed that the scalar potential equals the vector potential in order to obtain analytical solutions. Both radial and angular parts of the Dirac equation are solved using the Nikiforov–Uvarov method. A relativistic energy spectrum and the relation between quantum numbers can be obtained using this method. Several quantum wave functions corresponding to several states are also presented in terms of the Jacobi Polynomials.
Abstract Under the condition of the spin symmetry, we rigorously solve the Dirac equation with the q − deformed hyperbolic Pöschl-Teller potential plus a trigonometric Scarf II potential. According to the values of the deformation parameter q, four different cases are considered. For the two cases q ≥ 1 and q ≤ − 1 with 1 2 α ln q < r < + ∞ , the analytical energy spectra and the spinor wave functions associated with the l d − wave bound states are obtained using a suitable approximation to the centrifugal potential term. When 0 < q < 1 or −1 < q < 0, the spinor wave functions for the s − wave bound states are derived and we find that the quantization conditions are transcendental equations which can be solved numerically. The special case q = 0 is also discussed.
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.
The bound state solution of the Dirac equation for generalized Pöschl-Teller and trigonometric Pöschl-Teller non-central potentials was obtained using SUSY quantum mechanics and the idea of shape invariance potential.The approximate relativistic energy spectrum was expressed in the closed form.The radial and polar wave functions were obtained using raising and lowering of radial and polar operators.The orbital quantum numbers were found from the polar Dirac equation, which was solved using SUSY quantum mechanics and the idea of shape invariance.
Abstract This paper presents a general method to solve non-hermeticity potentials with PT (Parity-Time) symmetry using two first-order operators against η -weak-pseudo-hermiticity having position-dependent effective mass. It futher suggests a way to apply this method to Dirac equation with spinor wave functions and non-hermetic potentials with real energy spectrum considering position-dependent effective mass. To show the utilities this method was apply to some superpotentials such as Eckart, Scarf-II, Rosen-Mörse-II and Pöchl-Teller. Finally, it was shown that the real potentials can be converted to complex potentials with eigenvalues of a class of η -pseudo-hermeticity.