Bound states of \((1+1)\)-dimensional Dirac equation with kink-like vector potential and delta interaction. (English) Zbl 1338.81184
Summary: The relativistic problem of spin-1/2 fermions subject to vector hyperbolic (kink-like) potential \((\sim \operatorname{tanh}kx)\) is investigated by using the parametric Nikiforov-Uvarov method. The energy eigenvalue equation and the corresponding normalized wave functions are obtained in terms of the Jacobi polynomials in two cases.
MSC:
| 81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
| 81Q15 | Perturbation theories for operators and differential equations in quantum theory |
Keywords:
\((1+1)\)-dimensional Dirac equation; kink-like potential; Rosen-Morse potential; NU methodReferences:
| [1] | Abramowitz, M., Stegun, I. Handbook of mathematical function with formulas, graphs and mathematical tables. Dover, New York, 1964 · Zbl 0171.38503 |
| [2] | Akcay, H. Dirac equation with scalar and vector quadratic potentials and Coulomb-like tensor potential. Phys. Lett. A, 373: 616-620 (2009) · Zbl 1227.81152 · doi:10.1016/j.physleta.2008.12.029 |
| [3] | Antonio S., de Castro. Effects of a mixed vector-scalar kink-like potential for spinless particles in twodimensional space-time. Int. J. Mod. Phys. A, 22: 2609-2618 (2007); DOI: 10.1142/S0217751X07036828. · Zbl 1124.81014 · doi:10.1142/S0217751X07036828 |
| [4] | Antonio, S. de Castro A, Hott, M. Trapping neutral fermions with kink-like potentials. Phys. Lett. A, 351: 379 (2006) · doi:10.1016/j.physleta.2005.11.033 |
| [5] | Aydogdu, O., Sever, R. Exact solution of the Dirac equation with the Mie-type potential under the pseudospin and spin symmetry limit. Ann. Phys., 325: 373-383 (2010) · Zbl 1186.81049 · doi:10.1016/j.aop.2009.10.009 |
| [6] | Brittin, W.E. Lectures in theoretical physics, Vol. IV. Interscience Publishers, New York, 1962 · Zbl 0101.44101 |
| [7] | Eshghi, M. Dirac-hyperbolic Scarf problem including a Coulomb-like tensor potential. Acta Sci. Thech., 34(2): 207-215 (2012) |
| [8] | Eshghi, M., Hamzavi, M. Spin symmetry in Dirac-attractive Radial problem and tensor potential. Commun. Theor. Phys., 57: 355-360 (2012) · Zbl 1247.81113 · doi:10.1088/0253-6102/57/3/05 |
| [9] | Eshghi, M., Mehraban, H. Eigen spectra for Manning-Rosen potential including a Coulomb-like tensor interaction. Int. J. Phys. Sci., 16: 6643-6652 (2012) |
| [10] | Eshghi, M., Mehraban, H. Eigen spectra in Dirac-hyperbolic problem plus tensor coupling. Chin. J. Phys., 50(4): 533-543 (2012) · Zbl 07845002 |
| [11] | Eshghi, M., Mehraban, H. Solution of the Dirac equation with position-dependent mass for q-parameter modified Poschl-Teller and Coulomb-like tensor potential. Few-Body Syst., 52: 41-47 (2012) · doi:10.1007/s00601-011-0238-5 |
| [12] | Greiner, W. Relativistic Quantum Mechanics, Wave Equations. Springer-Verlag, New York, 1990 · Zbl 0718.35078 · doi:10.1007/978-3-662-02634-2 |
| [13] | Ikhdair, S.M. Rotational and vibrational diatomic molecule in the Klein-Gordon equation with hyperbolic scalar and vector potentials. Int. J. Mod. Phys. C, 20(10): 1563-1582 (2009) · Zbl 1180.81058 · doi:10.1142/S0129183109014606 |
| [14] | Ikhdair, S.M. Rotation and vibration of diatomic molecule in the spatially-dependent mass Schrödinger equation with generalized q-deformed Morse potential. Chem. Phys., 361: 9-17 (2009) · doi:10.1016/j.chemphys.2009.04.023 |
| [15] | Jia, C.-S. de Souza Dutra, A. Extension of PT-symmetric quantum mechanics to the Dirac theory with position-dependent mass. Ann. Phys., 323: 566-579 (2008) · Zbl 1350.81015 · doi:10.1016/j.aop.2007.04.007 |
| [16] | Jia, C.-S., de Souza Dutra, A. Position-dependent effective mass Dirac equations with PT-symmetric and non-PT-symmetric potentials. J. Phys. A: Math. Gen., 39: 11877 (2006); doi:10.1088/0305-4470/39/38/013 · Zbl 1100.81018 · doi:10.1088/0305-4470/39/38/013 |
| [17] | Jia, C.-S., Diao, Yong-Feng, Liu Jian-Yi. Bounded solutions of the Dirac equation with a PT-symmetric kink-like vector potential in two-dimensional space-time. Int. J. Theor. Phys., 47: 2513-2522 (2008) · Zbl 1157.81320 · doi:10.1007/s10773-008-9685-2 |
| [18] | Jia, C.-S., Li, Xiao-Ping, Zhang, Lie-Hui. Exact solutions of the Klein-Gordon equation with positiondependent mass for mixed vector and scalar kink-like potentials. Few Body Syst., 52: 11-18 (2012) · doi:10.1007/s00601-011-0258-1 |
| [19] | Katsnelson, M.I., Novoselov, K.S., Geim, A.K. Chiral Tunnelling and the Klein Paradox in Graphene. Nature Phys., 2: 620-625 (2006) · doi:10.1038/nphys384 |
| [20] | Luis, A.G.-D., Victor, M.V. Resonances in the one-dimensional Dirac equation in the presence of a point interaction and a constant electric field. Phys. Lett. A, 352: 202-205 (2006) · Zbl 1187.81105 · doi:10.1016/j.physleta.2005.12.003 |
| [21] | Magnus, W., Oberhenttinger, F., Soni, R.P. Formulas and theorems for the special functions of mathematical physics, 3Ed. Springer, Berlin, 1966 · Zbl 0143.08502 · doi:10.1007/978-3-662-11761-3 |
| [22] | Nikiforov, A.F., Uvarov, V.B. Special Functions of Mathematical Physics. Birkhauser Verlag, Basel, 1988 · Zbl 0624.33001 · doi:10.1007/978-1-4757-1595-8 |
| [23] | Peng, X.-L. Liu, J.-Y. Jia, C.-S. Approximation solution of the Dirac equation with position-dependent mass for the generalized Hulthen potential. Phys. Lett. A, 352: 478-483 (2006) · Zbl 1187.81110 · doi:10.1016/j.physleta.2005.12.039 |
| [24] | Ryder, L.H. Quantum Field Theory. Cambridge University Press, Cambridge, 1985 · Zbl 0555.46038 |
| [25] | Salamin, Y.I., Hu, S., Hatsagortsyan, K.Z., Keitel, Ch.. Relativistic high-power laser-matter interactions. Phys. Rep., 427(2-3): 41-155 (2006) · doi:10.1016/j.physrep.2006.01.002 |
| [26] | Tezcan, C., Sever, R. A General Approach for the Exact Solution of the Schrödinger Equation. Int. J. Theor. Phys., 48: 337-350 (2009) · Zbl 1162.81369 · doi:10.1007/s10773-008-9806-y |
| [27] | Tian, W.-J. Bound state for spin-0 and spin-1/2 particles with vector and scalar hyperbolic tangent and cotangent potentials. http://www.paper.edu.cn |
| [28] | Titchmarsh, E C. Eigenfunction expansions associated with second order differential equations, part II, Be deleted ands be revised as: Clarendon Press, Oxford, 1958 · Zbl 0097.27601 |
| [29] | Victor, M.V., Luis, A.G.-D. Particle resonance in the Dirac equation in the presence of a delta interaction and perturbative hyperbolic potential. Europ. Phys. J. C., 61(3): 519-525 (2009); ArXiv: 0903.2597v2 [hep-th] 25 Mar 2009 · doi:10.1140/epjc/s10052-009-0999-x |
| [30] | Wang, I.C., Wong, C.Y. Finite-size effect in the Schwinger particle-production mechanism. Phys. Rev. D., 38: 348-359 (1988) · doi:10.1103/PhysRevD.38.348 |
| [31] | Zarrinkamar, S., Rajabi, A.A., Hassanabadi, H. Dirac equation for the harmonic Scalar and vector potentials and linear plus Coulomb-like tensor potential; the SUSY approach. Ann. Phys., 325: 2522-2528 (2010) · Zbl 1200.81059 · doi:10.1016/j.aop.2010.05.013 |
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