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The energy eigenvalues of the exponential cosine screened Coulomb potential with magnetic field

Year 2013, Volume: 3 Issue: 2, 32 - 38, 23.12.2013
https://doi.org/10.17678/beuscitech.47128

Abstract

In the present study, we examine two dimensional solution of the Schrödinger equation for the exponential cosine screened Coulomb potential in a magnetic field. We apply the asymptotic iteration method to obtain energy eigenvalues. Since this equation has no analytical solution, the energy eigenvalues have been numerically obtained for different screening parameter, the Larmor frequency and the strength coupling constant. Effect of the magnetic field on the energy eigenvalues is precisely presented.

References

  • Aygun M, Bayrak O, Boztosun I, Sahin Y (2012). The energy eigenvalues of the kratzer potential in the presence of a magnetic field. Eur Phys J D 66, 35.
  • Aygun M, Sahin Y, Boztosun I (2010). Examination of V (r) =-Z/r + gr + λr2 potential in the presence of magnetic field. Int J Mod Phys E 19, 1349.
  • Bayrak O, Boztosun I (2006). Arbitrary ℓ-state solutions of the rotating morse potential by the asymptotic iteration method. J Phys A Math Gen 39, 6955.
  • Bayrak O, Boztosun I (2007). Application of the asymptotic iteration method to the exponential cosine screened coulomb potential. Int J Quant Chem 107, 1040-1045.
  • Blanter YM, Kaputkina NE, Lozovic YE (1996). Two- electron quantum dots in magnetic field. Phys Scr 54, 539.
  • Bonch-Bruevich VL, Glasko VB (1959). Sov. Phys. Dokl. 4, 147.
  • Bonch-Bruevich VL, Kogan SM (1960). The theory of electron plasma in semiconductors. Sov Phys Solid State 1, 1118.
  • Chatterjee A (1987). Hypervirial 1/N expansion for the bound-state energy spectrum of the generalized exponential-cosine-screened coulomb potential. Phys Rev A 35, 2722.
  • Ciftci H, Hall RL, Saad N (2003). Asymptotic iteration method for eigenvalue problems. J Phys A Math Gen 36, 11807.
  • Meyer H, Fack V, Berghe GV (1985). Dynamical group approach to the exponential cosine screened Coulomb potential. J Phys A 18, 849.
  • Demel T, Heitmann D, Grambow P, Ploog K (1990). Nonlocal dynamic response and level crossings in quantum-dot structures. Phys Rev Lett 64, 788.
  • Dutt R, Chowdhury K, Varshni YP (1985). An improved calculation for screened coulomb potentials in Rayleigh-Schrodinger perturbation theory. J Phys A 18, 1379.
  • Dutt R, Mukherji U, Varshni YP (1986). Energy levels and oscillator strengths for the exponential-cosine screened coulomb potential in the shifted large- dimension expansion theory. J Phys B At Mol Phys 19, 3411.
  • Fack V, Meyer H, Berghe GV (1986). The exponential cosine screened coulomb potential in the framework of algebraic perturbation theory. J Phys A Math Gen 19, 709-713.
  • Fernandez FM (2004). On an iteration method for eigenvalue problems. J Phys A Math Gen 37, 6173.
  • Hall GL (1962). Ionized impurity scattering in semiconductors. Phys Chem Solid 23, 1147.
  • Ikhdair SM, Sever R (1993). Bound-states of the exponential-cosine-screened coulomb potential. Z Phys D 28, 1.
  • Ikhdair SM, Sever R (2007). Bound energy of the exponential-cosine-screened coulomb potential. J Math Chem 41, 329-341.
  • Johnson NF (1995). Quantum dots: few-body, low- dimensional systems. J Phys Condens Matter 7, 965.
  • Killingbeck JP, Jolicard G (2009). A multiple shooting method for the Zeeman effect. J Phys A Math Theor 42, 075303.
  • Lai CS (1982). Energies of the exponential cosine screened coulomb potential. Phys Rev A 26, 2245.
  • Lam CS, Varshni YP (1972). Bound eigenstates of the exponential cosine screened coulomb potential. Phys Rev A 6, 1391.
  • Nasser I, Abdelmonem MS, Abdel-Hady A (2011). J-Matrix approach coulomb potential. Phys Scr 84, 045001.
  • exponential-cosine-screened
  • Prokopev E P (1967). Sov. Phys. Solid State 9, 993.
  • Sever R, Tezcan C (1987). 1/N expansion for the exponential-cosine-screened coulomb potential. Phys Rev A 35, 2725.
  • Shukla PK, Eliasson B (2008). Localized plasmons in quantum plasmas. Phys Lett A 372, 2893.
  • Soylu A, Bayrak O, Boztosun I (2006). The energy eigenvalues of the two dimensional hydrogen atom in a magnetic field. Int J Mod Phys E 15, 1263.
  • Takimoto N (1959). On the Screening of Impurity Potential by conduction electrons. J Phys Soc Japan 14, 1142.
  • Taut M (1995). Two-dimensional hydrogen in a magnetic field: analytical solutions. J Phys A Math Gen 28, 2081.
  • Villalba VM, Pino R (1998). Analytic computation of the energy levels of a two-dimensional hydrogenic donor in a constant magnetic field. Phys Scr 58, 605.
  • Villalba VM, Pino R (2001). Energy spectrum of a relativistic two-dimensional hydrogen-like atom in a constant magnetic field of arbitrary strength. Phys E 10, 561.
  • Zhu JL, Wu J, Fu RT, Chen H, Kawazoe Y (1997). Size and shape effects of quantum dots on two-electron spectra. Phys Rev B 55, 1673.
Year 2013, Volume: 3 Issue: 2, 32 - 38, 23.12.2013
https://doi.org/10.17678/beuscitech.47128

Abstract

References

  • Aygun M, Bayrak O, Boztosun I, Sahin Y (2012). The energy eigenvalues of the kratzer potential in the presence of a magnetic field. Eur Phys J D 66, 35.
  • Aygun M, Sahin Y, Boztosun I (2010). Examination of V (r) =-Z/r + gr + λr2 potential in the presence of magnetic field. Int J Mod Phys E 19, 1349.
  • Bayrak O, Boztosun I (2006). Arbitrary ℓ-state solutions of the rotating morse potential by the asymptotic iteration method. J Phys A Math Gen 39, 6955.
  • Bayrak O, Boztosun I (2007). Application of the asymptotic iteration method to the exponential cosine screened coulomb potential. Int J Quant Chem 107, 1040-1045.
  • Blanter YM, Kaputkina NE, Lozovic YE (1996). Two- electron quantum dots in magnetic field. Phys Scr 54, 539.
  • Bonch-Bruevich VL, Glasko VB (1959). Sov. Phys. Dokl. 4, 147.
  • Bonch-Bruevich VL, Kogan SM (1960). The theory of electron plasma in semiconductors. Sov Phys Solid State 1, 1118.
  • Chatterjee A (1987). Hypervirial 1/N expansion for the bound-state energy spectrum of the generalized exponential-cosine-screened coulomb potential. Phys Rev A 35, 2722.
  • Ciftci H, Hall RL, Saad N (2003). Asymptotic iteration method for eigenvalue problems. J Phys A Math Gen 36, 11807.
  • Meyer H, Fack V, Berghe GV (1985). Dynamical group approach to the exponential cosine screened Coulomb potential. J Phys A 18, 849.
  • Demel T, Heitmann D, Grambow P, Ploog K (1990). Nonlocal dynamic response and level crossings in quantum-dot structures. Phys Rev Lett 64, 788.
  • Dutt R, Chowdhury K, Varshni YP (1985). An improved calculation for screened coulomb potentials in Rayleigh-Schrodinger perturbation theory. J Phys A 18, 1379.
  • Dutt R, Mukherji U, Varshni YP (1986). Energy levels and oscillator strengths for the exponential-cosine screened coulomb potential in the shifted large- dimension expansion theory. J Phys B At Mol Phys 19, 3411.
  • Fack V, Meyer H, Berghe GV (1986). The exponential cosine screened coulomb potential in the framework of algebraic perturbation theory. J Phys A Math Gen 19, 709-713.
  • Fernandez FM (2004). On an iteration method for eigenvalue problems. J Phys A Math Gen 37, 6173.
  • Hall GL (1962). Ionized impurity scattering in semiconductors. Phys Chem Solid 23, 1147.
  • Ikhdair SM, Sever R (1993). Bound-states of the exponential-cosine-screened coulomb potential. Z Phys D 28, 1.
  • Ikhdair SM, Sever R (2007). Bound energy of the exponential-cosine-screened coulomb potential. J Math Chem 41, 329-341.
  • Johnson NF (1995). Quantum dots: few-body, low- dimensional systems. J Phys Condens Matter 7, 965.
  • Killingbeck JP, Jolicard G (2009). A multiple shooting method for the Zeeman effect. J Phys A Math Theor 42, 075303.
  • Lai CS (1982). Energies of the exponential cosine screened coulomb potential. Phys Rev A 26, 2245.
  • Lam CS, Varshni YP (1972). Bound eigenstates of the exponential cosine screened coulomb potential. Phys Rev A 6, 1391.
  • Nasser I, Abdelmonem MS, Abdel-Hady A (2011). J-Matrix approach coulomb potential. Phys Scr 84, 045001.
  • exponential-cosine-screened
  • Prokopev E P (1967). Sov. Phys. Solid State 9, 993.
  • Sever R, Tezcan C (1987). 1/N expansion for the exponential-cosine-screened coulomb potential. Phys Rev A 35, 2725.
  • Shukla PK, Eliasson B (2008). Localized plasmons in quantum plasmas. Phys Lett A 372, 2893.
  • Soylu A, Bayrak O, Boztosun I (2006). The energy eigenvalues of the two dimensional hydrogen atom in a magnetic field. Int J Mod Phys E 15, 1263.
  • Takimoto N (1959). On the Screening of Impurity Potential by conduction electrons. J Phys Soc Japan 14, 1142.
  • Taut M (1995). Two-dimensional hydrogen in a magnetic field: analytical solutions. J Phys A Math Gen 28, 2081.
  • Villalba VM, Pino R (1998). Analytic computation of the energy levels of a two-dimensional hydrogenic donor in a constant magnetic field. Phys Scr 58, 605.
  • Villalba VM, Pino R (2001). Energy spectrum of a relativistic two-dimensional hydrogen-like atom in a constant magnetic field of arbitrary strength. Phys E 10, 561.
  • Zhu JL, Wu J, Fu RT, Chen H, Kawazoe Y (1997). Size and shape effects of quantum dots on two-electron spectra. Phys Rev B 55, 1673.
There are 33 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Murat Aygün This is me

Publication Date December 23, 2013
Submission Date October 16, 2013
Published in Issue Year 2013 Volume: 3 Issue: 2

Cite

IEEE M. Aygün, “The energy eigenvalues of the exponential cosine screened Coulomb potential with magnetic field”, Bitlis Eren University Journal of Science and Technology, vol. 3, no. 2, pp. 32–38, 2013, doi: 10.17678/beuscitech.47128.