Subscribe

Subscribe to our Newsletter and get informed about new publication regulary and special discounts for subscribers!

IFSL > Volume 10 > A Novel Exactly Theoretical Solvable of Bound...
< Back to Volume

A Novel Exactly Theoretical Solvable of Bound States of the Dirac-Kratzer-Fues Problem with Spin and Pseudo-Spin Symmetry

Full Text PDF

Abstract:

New exact bound state solutions of the deformed radial upper and lower components of Dirac equation and corresponding Hermitian anisotropic Hamiltonian operator are studied for the modified Kratzer-Fues potential (m.k.f.) potential by using Bopp’s shift method instead to solving deformed Dirac equation with star product. The corrections of energy eigenvalues are obtained by applying standard perturbation theory for interactions in one-electron atoms. Moreover, the obtained corrections of energies are depended on two infinitesimal parameters (θ, χ), which induced by position-position noncommutativity, in addition to the discreet nonrelativistic atomic quantum numbers: (j=l±1/1,s=±1/2,l and m) and we have also shown that, the usual relativistic states in ordinary three dimensional spaces are canceled and has been replaced by new degenerated 2(2l+1) sub-states in the extended quantum symmetries (NC: 3D-RS).

Info:

Periodical:
International Frontier Science Letters (Volume 10)
Pages:
8-22
DOI:
https://doi.org/10.18052/www.scipress.com/IFSL.10.8
Citation:
A. Maireche "A Novel Exactly Theoretical Solvable of Bound States of the Dirac-Kratzer-Fues Problem with Spin and Pseudo-Spin Symmetry", International Frontier Science Letters, Vol. 10, pp. 8-22, 2016
Online since:
Dec 2016
Authors:
Abdelmadjid Maireche
Keywords:
Bopp’s Shift Method, Dirac Equation, Kratzer-Fues Potential, Noncommutative Space, Star Product
Export:
RIS, BibTeX, Text
Distribution:
Open Access

Creative Commons License
This work is licensed under a
Creative Commons Attribution 4.0 International License

References:

[1] E. MAGHSOODI, H. HASSANABADI, O. AYDOǦDU, DIRAC PARTICLES IN THE PRESENCE OF THE YUKAWA POTENTIAL PLUS A TENSOR INTERACTION IN SUSYQM FRAMEWORK, PHYSICA SCRIPTA. 86(1) (2012) 015005.

DOI: https://doi.org/10.1088/0031-8949/86/01/015005

[2] E. MAGHSOODI ET AL., RELATIVISTIC SYMMETRIES OF THE DIRAC EQUATION UNDER THE NUCLEAR WOODS–SAXON POTENTIAL, PHYSICA SCRIPTA. 85(5) (2012) 055007.

DOI: https://doi.org/10.1088/0031-8949/85/05/055007

[3] M. Hamzavi, S.M. Ikhdair, B.I. Ita, Approximate spin and pseudospin solutions to the Dirac equation for the inversely quadratic Yukawa potential and tensor interaction, Physica Scripta. 85(4) (2012) 045009.

DOI: https://doi.org/10.1088/0031-8949/85/04/045009

[4] S.M. Ikhdair, B.J. Falaye, Approximate relativistic bound states of a particle in Yukawa field with Coulomb tensor interaction, Physica Scripta. 87(3) (2013) 035002.

DOI: https://doi.org/10.1088/0031-8949/87/03/035002

[5] S.M. Ikhdair, Approximate -state solutions of the Dirac equation in spatially dependent mass for the Eckart potential including the Yukawa tensor interaction, Physica Scripta. 88(6) (2013) 065007.

[6] S.H. Dong, Z.Q. Ma, Exact solutions to the Dirac equation with a Coulomb potential in 2+1 dimensions, Phys. Lett. A. 312 (2003) 78-83.

[7] S. Zarrinkamar, H. Hassanabadi, A.A. Rajabi, Dirac equation for a Coulomb scalar, vector and tensor interaction, Int. J. Mod. Phys. A. 26 (2011) 1011-1018.

[8] K.J. Oyewumi et al., k-state solutions for the fermionic massive spin-1/2 particles interacting with double ring-shaped Kratzer and oscillator potentials, Int. J. Mod. Phys. E. 23 (2014) 1450005.

DOI: https://doi.org/10.1142/s0218301314500050

[9] H. Hassanabadi, E. Maghsoodi, S. Zarrinkamar, Relativistic symmetries of Dirac equation and the Tietz potential, The European Physical Journal Plus. 127(3) (2012) 1-14.

DOI: https://doi.org/10.1140/epjp/i2012-12031-1

[10] M.R. Setare, S. Haidari, Spin symmetry of the Dirac equation with the Yukawa potential, Physica Scripta. 81 (2010) 065201.

DOI: https://doi.org/10.1088/0031-8949/81/06/065201

[11] A. Soylu, O. Bayrak, I. Boztosun, An approximate solution of the Dirac-Hulth_n problem with pseudospin and spin symmetry for any k state, J. Math. Phys. 48 (2007) 082302.

DOI: https://doi.org/10.1063/1.2768436

[12] C.A. Onate, J.O. Ojonubah, Relativistic and nonrelativistic solutions of the generalized Pӧschl- Teller and hyperbolical potentials with some thermodynamic properties, Int. J. Mod. Phys. E. 24(03) (2015) 1550020.

DOI: https://doi.org/10.1142/s0218301315500202

[13] S.M. Ikhdair, R. Sever, Approximate analytical solutions of the generalized Woods-Saxon potentials including the spin-orbit coupling term and spin symmetry, Cent. Eur. J. Phys. 8(4) (2010) 652-666.

DOI: https://doi.org/10.2478/s11534-009-0118-5

[14] S.M. Ikhdair, R. Sever, Approximate Eigenvalue and Eigenfunctions Solutions for the Generalized Hulthén Potential with any Angular Momentum, Journal of Mathematical Chemistry. 42(3) (2007) 461-471.

[15] M. Eshghia, S.M. Ikhdair, Relativistic effect of pseudospin symmetry and tensor coupling on the Mie-type potential via Laplace transformation method, Chin. Phys. B. 23(12) (2014) 120304.

[16] B. Biswas, S. Debnath, Bound States of the Dirac-Kratzer-Fues Problem with Spin and Pseudo-Spin Symmetry via Laplace Transform Approach, Bulg. J. Phys. 43 (2016) 89–99.

[17] H.S. Snyder, Quantized Space-Time, Phys. Rev. 71(1) (1947) 38-41.

[18] A. Connes, Noncommutative differential geometry, Publications mathématiques de l'IHÉS, 62(1) (1985) 41-144.

[19] A. Maireche, Atomic Spectrum for Schrödinger Equation with Rational Spherical Type Potential in Non-commutative Space and Phase, Afr. Rev Phys. 10 (2015) 373-381.

[20] A. Maireche, Spectrum of Hydrogen Atom Ground State Counting Quadratic Term in Schrödinger Equation, Afr. Rev Phys. 10 (2015) 177-183.

[21] A. Maireche, Deformed Bound States for Central Fraction Power Potential: Non Relativistic Schrödinger Equation, Afr. Rev Phys. 10 (2015) 97-103.

[22] A. Maireche, Spectrum of Schrödinger Equation with H.L.C. Potential in Non-commutative Two-dimensional Real Space, Afr. Rev Phys. 9 (2014) 479-485.

[23] A. Maireche, A Study of Schrödinger Equation with Inverse Sextic Potential in 2-dimensional Non-commutative Space, Afr. Rev Phys. 9 (2014) 185-193.

[24] A. Maireche, Nonrelativistic Atomic Spectrum for Companied Harmonic Oscillator Potential and its Inverse in both NC-2D: RSP, International Letters of Chemistry, Physics and Astronomy. 56 (2015) 1-9.

DOI: https://doi.org/10.18052/www.scipress.com/ilcpa.56.1

[25] A. Maireche, New Exact Solution of the Bound States for the Potential Family V(r)=A/r2-B/r+Crk (k=0, -1, -2) in both Noncommutative Three Dimensional Spaces and Phases: Non Relativistic Quantum Mechanics, International Letters of Chemistry, Physics and Astronomy. 58 (2015).

[26] A. Maireche, A New Approach to the Non Relativistic Schrödinger Equation for an Energy-Depended Potential in both Noncommutative Three Dimensional Spaces and Phases, International Letters of Chemistry, Physics and Astronomy. 60 (2015) 11-19.

DOI: https://doi.org/10.18052/www.scipress.com/ilcpa.60.11

[27] A. Maireche, A New Study to the Schrödinger Equation for Modified Potential V(r)=ar2+ br-4+cr-6 in Nonrelativistic Three Dimensional Real Spaces and Phases, International Letters of Chemistry, Physics and Astronomy. 61 (2015) 38-48.

[28] A. Maireche, A New Nonrelativistic Investigation for the Lowest Excitations States of Interactions in One-Electron Atoms, Muonic, Hadronic and Rydberg Atoms with Modified Inverse Power Potential, International Frontier Science Letters. 9 (2016).

DOI: https://doi.org/10.18052/www.scipress.com/ifsl.9.33

[29] A. Maireche, Deformed Quantum Energy Spectra with Mixed Harmonic Potential for Nonrelativistic Schrödinger equation, J. Nano-Electron. Phys. 7(2) (2015) 02003-1 - 02003-6.

[30] A. Maireche, A Recent Study of Quantum Atomic Spectrum of the Lowest Excitations for Schrödinger Equation with Typical Rational Spherical Potential at Planck's and Nanoscales, J. Nano- Electron. Phys. 7(3) (2015) 03047-1 - 03047-7.

[31] A. Maireche, Quantum Hamiltonian and Spectrum of Schrödinger Equation with companied Harmonic Oscillator Potential and its Inverse in three Dimensional Noncommutative Real Space and Phase, J. Nano- Electron. Phys. 7(4) (2015) 04021-1 - 04021-7.

[32] A. Maireche, New Relativistic Atomic Mass Spectra of Quark (u, d and s) for Extended Modified Cornell Potential in Nano and Plank's Scales, J. Nano- Electron. Phys. 8(1) (2016) 01020-1 - 01020-7.

DOI: https://doi.org/10.21272/jnep.8(1).01020

[33] A. Maireche, The Nonrelativistic Ground State Energy Spectra of Potential Counting Coulomb and Quadratic Terms in Non-commutative Two Dimensional Real Spaces and Phases, J. Nano- Electron. Phys. 8(1) (2016) 01021-1 - 01021-6.

[34] A. Maireche, New Theoretical Study of Quantum Atomic Energy Spectra for Lowest Excited States of Central (PIHOIQ) Potential in Noncommutative Spaces and Phases Symmetries at Plan's and Nanoscales, J. Nano- Electron. Phys. 8(2) (2016).

DOI: https://doi.org/10.21272/jnep.8(2).02027

[35] A. Maireche, A New Nonrelativistic Atomic Energy Spectrum of Energy Dependent Potential for Heavy Quarkouniom in Noncommutative Spaces and Phases Symmetries, J. Nano- Electron. Phys. 8(2) (2016) 02046-1 - 02046-6.

DOI: https://doi.org/10.21272/jnep.8(2).02046

[36] A. Maireche, New exact bound states solutions for (C.F.P.S. ) potential in the case of Non-commutative three dimensional non relativistic quantum mechanics, Med. J. Model. Simul. 04 (2015) 060-072.

[37] A. Maireche, New Bound State Energies for Spherical Quantum Dots in Presence of a Confining Potential Model at Nano and Plank's Scales, NanoWorld J. 1(4) (2016) 120-127.

DOI: https://doi.org/10.17756/nwj.2016-016

[38] A. Maireche, Quantum Schrödinger equation with Octic potential in non-commutative two-dimensional complex space, Life Sci J. 11(6) (2014) 353-359.

[39] A. Maireche, New quantum atomic spectrum of Schrödinger equation with pseudo harmonic potential in both noncommutative three dimensional spaces and phases, Lat. Am. J. Phys. Educ. 9(1) (2015) 1301.

[40] A. Maireche, D. Imane, A New Nonrelativistic Investigation for Spectra of Heavy Quarkonia with Modified Cornell Potential: Noncommutative Three Dimensional Space and Phase Space Solutions, J. Nano-Electron. Phys. 8(3) (2016) 03025-1.

DOI: https://doi.org/10.21272/jnep.8(3).03025

[41] A. Maireche, A Complete Analytical Solution of the Mie-Type Potentials in Non-commutative 3-Dimensional Spaces and Phases Symmetries, Afr. Rev Phys. 11 (2016) 111-117.

[42] A. Maireche, New Exact Energy Eigen-values for (MIQYH) and (MIQHM) Central Potentials: Non-relativistic Solutions, Afr. Rev Phys. 11 (2016) 175-185.

[43] A. Maireche, A New Relativistic Study for Interactions in One-electron atoms (Spin ½ Particles) with Modified Mie-type Potential, J. Nano-Electron. Phys. 8(4) (2016) 04027-1 - 04027-9.

[44] T. Curtright, D. Fairlie, C.K. Zachos, Features of time independent Wigner functions, Phys. Rev. D. 58(2) (1998) 025002.

DOI: https://doi.org/10.1103/physrevd.58.025002

[45] J. Gamboa, M. Loewe, J.C. Rojas, Noncommutative quantum mechanics, Phys. Rev. D. 64(6) (2001) 067901.

[46] L. Mezincescu, Star operation in quantum mechanics, Unpublished paper, arXiv preprint hep-th/0007046v2, (2000).

[47] Y. Yi et al., Spin-1/2 relativistic particle in a magnetic field in NC phase space, Chinese Physics C. 34(5) (2010) 543-547.

[48] A.E.F. Djemei, H. Smail, On Quantum Mechanics on Noncommutative Quantum Phase Space, Communications in Theoretical Physics. 41(6) (2004) 837-844.

[49] S. Cai, T. Jing, Dirac Oscillator in Noncommutative Phase Space, Int. J. Theor. Phys. 49(8) (2010) 1699-1705.

[50] J. Lee, Star Products and the Landau Problem, Journal of the Korean Physical Society. 47(4) (2005) 571-576.

[51] A.F. Dossa, G.Y.H. Avossevou, Noncommutative phase space and the two dimensional quantum dipole in background electric and magnetic fields, Journal of Modern Physics. 4(10) (2013) 1400-1411.

[52] Z.H. Yang et al., DKP Oscillator with Spin-0 in Three-dimensional Noncommutative Phase Space, Int. J. Theor. Phys. 49 (2010) 644-657.

[53] J. Mamat; S. Dulat, H. Mamatabdulla, Landau-like Atomic Problem on a Non-commutative Phase Space, Int. J. Theor. Phys. 55 (2016) 2913–2918.

[54] B. Mirza et al., Relativistic Oscillators in a Noncommutative Space and in a Magnetic Field, Commun. Theor. Phys. 55 (2011) 405-409.

[55] Y. Xiao; Z. Long, S. Cai, Klein-Gordon Oscillator in Noncommutative Phase Space Under a Uniform Magnetic Field, Int. J. Theor. Phys. 50 (2011) 3105-3111.

[56] A. Al-Jamel, Heavy quarkonia with Cornell potential on noncommutative space, Journal of Theoretical and Applied Physics. 5(1) (2011) 21-24.

[57] H. Hassanabadi, F. Hoseini, S. Zarrinkamar, A generalized interaction in noncommutative space: Both relativistic and nonrelativistic fields, Eur. Phys. J. Plus. 130(10) (2015) 1-7.

[58] W.S. Chung, Two Dimensional Non-commutative Space and Rydberg Atom Mode, Int. J. Theor. Phys. 54(6) (2015) 1840-1849.

DOI: https://doi.org/10.1007/s10773-014-2389-x

[59] M.M. Nieto, L.M. Simmons Jr., Eigenstates, Coherent States, and Uncertainty Products for the Morse Oscillator, Phys. Rev. A. 19(2) (1979) 438–444.

DOI: https://doi.org/10.1103/physreva.19.438

[60] M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover Publications, New York, (1965).

[61] S.H. Dong, G.H. Sun, The Schrödinger Equation with a Coulomb Plus Inverse-Square Potential in D Dimensions, Phys. Scr. 70(2-3) (2004) 94-97.

DOI: https://doi.org/10.1088/0031-8949/70/2-3/004
Show More Hide