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Journal of Scientific Research

Eigen Spectra for q-Deformed Hyperbolic Scarf Potential Including a Coulomb-like Tensor Interaction

M. Eshghi, Hossein Mehraban

Published Apr 28, 2011• 8 citations
Publisher

Abstract

We study the Dirac equation for the q-deformed hyperbolic Scarf potential including a coulomb-like tensor potential under the spin symmetry. The parametric generalization of the Nikiforov-Uvarov method is used to obtain the energy eigenvalues equation and the unnormalized wave functins.Keywords: Dirac equation; q-deformed hyperbolic Scarf; Spin symmetry; Tensor coupling.© 2011 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.doi:10.3329/jsr.v3i2.7295 J. Sci. Res. 3 (2), 239-247 (2011)

DOI
10.3329/jsr.v3i2.7295

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We study the Dirac equation for the q-deformed hyperbolic Scarf potential including a coulomb-like tensor potential under the spin symmetry. The parametric generalization of the Nikiforov-Uvarov method is used to obtain the energy eigenvalues equation and the unnormalized wave functins.Keywords: Dirac equation; q-deformed hyperbolic Scarf; Spin symmetry; Tensor coupling.© 2011 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.doi:10.3329/jsr.v3i2.7295 J. Sci. Res. 3 (2), 239-247 (2011)
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.
The bound state solutions of Dirac equation for q-deformed trigonometric Scarf potential with q-deformed trigonometric cotangent and cosecant tensor coupling potential under spin and pseudospin symmetric limits are investigated using Supersymmetric Quantum Mechanics (SUSY QM) method. The new tensor potentials proposed is inspired by superpotential form in SUSY quantum mechanics. The Dirac equations for Scarf potential coupled by new tensor potential in the pseudospin and spin symmetric cases reduce to Schrodinger type equations for shape invariant potential since the proposed new potentials are equivalent to the superpotential of q-deformed trigonometric Scarf potential. The relativistic wave functions are exactly obtained by using SUSY operator method and the relativistic energy equation are exactly obtained by using SUSY method and the idea of shape invariance in the approximation scheme of centrifugal term. The new tensor potential causes the energy degeneracies is omit both for pseudospin and spin symmetric case.
Abstract In this paper, the Dirac equation with the q-deformed Scarf potential for spin symmetry is solved for an arbitrary spin-orbit quantum number κ, in the presence of Coulomb-like potential tensor. Using the Feynman path integral formalism and the Pekeris approximation of the centrifugal term, we obtain the bound state energy eigenvalues and the associated spinor of the Dirac particle. Furthermore, this method is used to determine the spectrum of two diatomic molecules Li 2(61Π u ) and KRb(B −1Π). The obtained results are compared to the experimental and numerical ones.
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.