New Bound States for Modified Vibrational-Rotational Structure of Supersingular Plus Coulomb Potential of the Schrödinger Equation in One-Electron Atoms

Maireche, Abdelmadjid

doi:10.18052/www.scipress.com/ILCPA.73.31

ILCPA > Volume 73 > New Bound States for Modified...

< Back to Volume

New Bound States for Modified Vibrational-Rotational Structure of Supersingular Plus Coulomb Potential of the Schrödinger Equation in One-Electron Atoms

Full Text PDF

Abstract:

In this study, three-dimensional modified time-independent Schrödinger equation of modified vibrational-rotational structure of supersingular plus Coulomb (v.r.s.c) potential was solved using Boopp’s shift method instead to apply star product, in the framework of both noncommutativity three dimensional real space and phase (NC: 3D-RSP). We have obtained the explicit energy eigenvalues for ground state and first excited state for interactions in one-electron atoms. Furthermore, the obtained corrections of energies are depended on infinitesimal parameters (Θ,χ) and (θ,σ) which are induced by position-position and momentum-momentum noncommutativity, respectively, in addition to the discreet atomic quantum numbers: j=l±1/2,s=±1/2,l and the angular momentum quantum number m. We have also shown that, the usual states in ordinary three dimensional spaces for ordinary vibrational-rotational structure of supersingular plus Coulomb potential are canceled and has been replaced by new degenerated 2(2l+1) sub-states in the extended new quantum symmetries of (NC: 3D-RSP).

Info:

Periodical:

International Letters of Chemistry, Physics and Astronomy (Volume 73)

Pages:

31-45

DOI:

https://doi.org/10.18052/www.scipress.com/ILCPA.73.31

Citation:

A. Maireche, "New Bound States for Modified Vibrational-Rotational Structure of Supersingular Plus Coulomb Potential of the Schrödinger Equation in One-Electron Atoms", International Letters of Chemistry, Physics and Astronomy, Vol. 73, pp. 31-45, 2017

Online since:

April 2017

Authors:

Abdelmadjid Maireche

Keywords:

Boopp’s Shift Method, Noncommutative Phase, Noncommutative Space, Star Product, Vibrational-Rotational Structure of Supersingular Plus Coulomb Potential

Export:

RIS, BibTeX, Text

Distribution:

Open Access

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

References:

[1] S. -H. Dong, G. -H. Sun, The Schrödinger equation with a Coulomb plus inverse-square potential in D dimensions, Physica Scripta. 70(2-3) (2004) 94–97.

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

[2] D.L. Aronstein, C.R. Stroud, Jr., General series solution for finite square-well energy levels for use in wave-packet studies, Am. J. Phys. 68 (2000) 943–949.

DOI: https://doi.org/10.1119/1.1285868

[3] L. Buragohain, S.A.S. Ahmed, Exactly solvable quantum mechanical systems generated from the anharmonic potentials, Lat. Am. J. Phys. Educ. 4(1) (2010) 79–83.

[4] R.J. Lombard, J. Mars, C. Volpe, Wave equations of energy dependent potentials for confined systems, Journal of Physics G: Nuclear and Particle Physics. 34 (2007) 1879–1888.

[5] K.J. Oyewumi, E.A. Bangudu, Isotropic harmonic oscillator plus inverse quadratic potential in N-dimensional space, The Arabian Journal for Science and Engineering. 28(2A) (2003) 173.

[6] M.M. Nieto, Hydrogen atom and relativistic pi-mesic atom in N-space dimension, Am. J. Phys. 47 (1979) 1067–1072.

DOI: https://doi.org/10.1119/1.11976

[7] S.M. Ikhdair, R. Sever, Exact polynomial eigensolutions of the Schrödinger equation for the pseudoharmonic potential, Journal of Molecular Structure: THEOCHEM. 806(1) (2007) 155–158.

DOI: https://doi.org/10.1016/j.theochem.2006.11.019

[8] A.S. Ahmed, L. Buragohain, Generation of new classes of exactly solvable potentials, Phys. Scr. 80 (2009) 1–6.

DOI: https://doi.org/10.1088/0031-8949/80/02/025004

[9] S.K. Bose, Exact solution of non-relativistic Schrödinger equation for certain central physical potentials, Nouvo Cimento B. 113 (1996) 299–328.

[10] G.P. Flesses, A. Watt, An exact solution of the Schrödinger equation for a multiterm potential, J. Phys. A: Math. Gen. 14 (1981) L315–L318.

DOI: https://doi.org/10.1088/0305-4470/14/9/001

[11] M. Yildiz, Energy levels and atomic lifetimes of Rydberg states in neutral Indium, Acta Physica Polonica A. 123(1) (2013) 25–30.

DOI: https://doi.org/10.12693/aphyspola.123.25

[12] S.H. Dong, Schrödinger equation with the potential V(r) =Ar−4+Br−3+Cr−2+Dr−1, Physica Scripta. 64(4) (2001) 273–276.

[13] D. Mikulski et al., Exact solution of the Schrödinger equation with a new expansion of anharmonic potential with the use of the supersymmetric quantum mechanics and factorization method, J. Math. Chem. 53 (2015) 2018–(2027).

DOI: https://doi.org/10.1007/s10910-015-0532-4

[14] S.H. Dong, A new approach to the relativistic Schrödinger equation with central potential: Ansatz method, International Journal of Theoretical Physics. 40(2) (2001) 559–567.

[15] A.A. Rajabi, M. Hamzavi et al., A new Coulomb ring-shaped potential via generalized parametetric Nikivforov-Uvarov method, Journal of Theoretical and Applied Physics. 7(1) (2013) 1–15.

[16] B. Biswas, S. Debnath, Bound states for pseudoharmonic potential of the Dirac equation with spin and pseudo-spin symmetry via Laplace transform approach, Acta Physica Polonica A. 130(3) (2016) 692–696.

DOI: https://doi.org/10.12693/aphyspola.130.692

[17] S. -H. Dong, G. -H. San, Quantum spectrum of some anharmonic central potentials: wave functions ansatz, Foundations of Physics Letters. 16(4) (2003) 357–367.

[18] L. Buragohain, S.A.S. Ahmed, Exactly solvable quantum mechanical systems generated from the anharmonic potentials, Lat. Am. J. Phys. Educ. 4(1) (2010) 79-83.

[19] S.M. Ikhdair, Exact solution of Dirac equation with charged harmonic oscillator in electric field: bound states, Journal of Modern Physics. 3(2) (2012) 170–179.

DOI: https://doi.org/10.4236/jmp.2012.32023

[20] Zhang Tian-Yi, Zheng Neng-Wu, Theoretical study of energy levels and transition probabilities of boron atom, Acta Physica Polonica A. 116(2) (2009) 141–153.

DOI: https://doi.org/10.12693/aphyspola.116.141

[21] H. Hassanabadi et al., Exact solutions of N-dimensional Schrödinger equation for a potential containing coulomb and quadratic terms, International Journal of the Physical Sciences. 6(3) (2011) 583–586.

[22] S. -H. Dong, Z. -Q. Ma, G. Esposito, Exact solutions of the Schrödinger equation with inverse-power potential, Foundations of Physics Letters. 12(5) (1999) 465–473.

[23] D. Agboola, Complete analytical solutions of the Mie-Type potentials in N-dimensions, Acta Physica Polonica A. 120 (2011) 371–377.

DOI: https://doi.org/10.12693/aphyspola.120.371

[24] D. Shi-Hai, Exact solutions of the two-dimensional Schrödinger equation with certain central potentials, Int. J. Theor. Phys. 39 (2000) 1119–1128.

[25] B.I. Ita, Solutions of the Schrödinger equation with inversely quadratic Hellmann plus Mie-type potential using Nikiforov-Uvarov method, International Journal of Recent Advances in Physics. 2(4) (2013).

DOI: https://doi.org/10.1063/1.4902294

[26] P. Gupta, I. Mehrotra, Study of heavy quarkonium with energy dependent potential, Journal of Modern Physics. 3 (2012) 1530–1536.

DOI: https://doi.org/10.4236/jmp.2012.310189

[27] B.I. Ita, A.I. Ikeuba, A.N. Ikot, Solutions of the Schrödinger equation with quantum mechanical gravitational potential plus harmonic oscillator potential, Commun. Theor. Phys. 61(2) (2014) 149.

DOI: https://doi.org/10.1088/0253-6102/61/2/01

[28] A. Ghoshal, Y.K. Ho, Ground states of helium in exponential-cosine-screened Coulomb potentials, Journal of Physics B: Atomic, Molecular and Optical Physics. 42(7) (2009).

DOI: https://doi.org/10.1088/0953-4075/42/7/075002

[29] S.M. Kuchin, N.V. Maksimenko, Theoretical estimations of the spin-averaged mass spectra of heavy quarkonia and Bc mesons, Universal Journal of Physics and Applications. 1(3) (2013) 295–298.

[30] H. Egrifes, D. Demirhan, F. Buyukkilic, Exact solutions of the Schrödinger equation for the deformed hyperbolic potential well and the deformed four-parameter exponential type potential, Phys. Lett. A. 275 (2000) 229.

DOI: https://doi.org/10.1016/s0375-9601(00)00592-2

[31] V.C. Aguilera-Navarro, E. Ley-Koo, S. Mateos-Cortés, Vibrational–rotational analysis of supersingular plus quadratic potential , Int. J. Theor. Phys. 40(10) (2001) 157–166.

DOI: https://doi.org/10.1007/bf02435778

[32] V.C. Aguilera-Navarro, E. Ley-Koo, S. Mateos-Cortés, Vibrational–rotational structure of supersingular plus Coulomb potential , Int. J. Theor. Phys. 36(01) (1997) 1809–1816.

DOI: https://doi.org/10.1007/bf02435778

[33] H. Snyder, The Quantization of space time, Phys. Rev. 71 (1946) 38–41.

[34] A. Maireche, Spectrum of hydrogen atom ground state counting quadratic term in Schrödinger equation, Afr. Rev Phys. 10 (2015) 177–183.

[35] A. Maireche, Deformed bound states for central fraction power potential: non relativistic Schrödinger equation, Afr. Rev Phys. 10 (2015) 97–103.

[36] 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.

[37] A. Maireche, A study of Schrödinger equation with inverse sextic potential in 2-dimensional non-commutative space, Afr. Rev Phys. 9 (2014) 185–193.

[38] 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.

[39] A. Maireche, Atomic spectrum for Schrödinger equation with rational spherical type potential in non-commutative space and phase, Afr. Rev Phys. 10 (2016) 373–381.

[40] 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

[41] 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).

DOI: https://doi.org/10.18052/www.scipress.com/ilcpa.58.164

[42] 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

[43] A. Maireche, A new study to the Schrödinger equation for modified potential in nonrelativistic three dimensional real spaces and phases, International Letters of Chemistry, Physics and Astronomy. 61 (2015) 38–48.

DOI: https://doi.org/10.18052/www.scipress.com/ilcpa.61.38

[44] 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

[45] 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.

[46] 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.

[47] 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) 04021-104021-7.

[48] 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

[49] 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.

DOI: https://doi.org/10.21272/jnep.8(1).01021

[50] 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

[51] 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

[52] 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.

[53] 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) 122–129.

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

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

[55] 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.

[56] A.E.F. Djemei, H. Smail, On quantum mechanics on noncommutative quantum phase space, Commun. Theor. Phys. 41 (2004) 837–844.

DOI: https://doi.org/10.1088/0253-6102/41/6/837

[57] S. Cai et al., Dirac oscillator in noncommutative phase space, Int. J. Theor. Phys. 49(8) (2010) 1699–1705.

[58] J. Lee, Star products and the Landau problem, Journal of the Korean Physical Society. 47(4) (2005) 571–576.

[59] A. Jahan, Noncommutative harmonic oscillator at finite temperature: a path integral approach, Brazilian Journal of Physics. 37(4) (2007) 144–146.

DOI: https://doi.org/10.1590/s0103-97332008000100026

[60] 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 (2013) 1400–1411.

DOI: https://doi.org/10.4236/jmp.2013.410168

[61] Z. -H. Yang et al., DKP oscillator with spin-0 in three dimensional noncommutaive phase space, Int. J. Theor. Phys. 49 (2010) 644–657.

[62] Y. Yuan et al., Spin ½ relativistic particle in a magnetic field in NC phase space, Chinese Physics C. 34(5) (2010) 543.

[63] J. Mamat, S. Dulat, H. Mamatabdulla, Landau-like atomic problem on a non-commutative phase space, Int. J. Theor. Phys. 55 (2016) 2913–2918.

DOI: https://doi.org/10.1007/s10773-016-2922-1

[64] B. Mirza et al., Relativistic oscillators in a noncommutative space in a magnetic field, Commun. Theor. Phys. 55 (2011) 405–409.

DOI: https://doi.org/10.1088/0253-6102/55/3/06

[65] 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.

DOI: https://doi.org/10.1007/s10773-011-0811-1

[66] A.E.F. Djemaï, H. Smail, On quantum mechanics on noncommutative quantum phase space, Commun. Theor. Phys. 41 (2004) 837.

DOI: https://doi.org/10.1088/0253-6102/41/6/837

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

[68] I.S. Gradshteyn, I.M. Ryzhik, Table of integrals, Series and Products, 7th. ed., Elsevier, (2007).

Show More Hide

Cited By:

[1] A. Maireche, "Effects of Two-Dimensional Noncommutative Theories on Bound States Schrödinger Diatomic Molecules under New Modified Kratzer-Type Interactions", International Letters of Chemistry, Physics and Astronomy, Vol. 76, p. 1, 2017

DOI: https://doi.org/10.18052/www.scipress.com/ILCPA.76.1

[2] O. Hegacy, "Model for End-Stage Liver Disease (Meld) Score, As a Prognostic Factor for Cirrhotic Patients, Undergoing Hepatectomy for Hepatocellular Carcinoma", Gastroenterology & Hepatology : Open Access, Vol. 2, 2015

DOI: https://doi.org/10.15406/ghoa.2015.02.00044