Subscribe

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

ILCPA > ILCPA Volume 76 > Effects of Two-Dimensional Noncommutative Theories...
< Back to Volume

Effects of Two-Dimensional Noncommutative Theories on Bound States Schrödinger Diatomic Molecules under New Modified Kratzer-Type Interactions

Full Text PDF

Abstract:

In this work, an analytical expression for the nonrelativistic energy spectrum of some diatomic molecules was obtained through the Bopp’s shift method in the noncommutative (NC) two-dimensional real space-phase symmetries (NC: 2D-RSP) with a new modified Kratzer-type potential (NMKP) in the framework of two infinitesimal parameters and due to (space-phase) noncommutativity, by means of the solution of the noncommutative Schrödinger equation. The perturbation property of the spin-orbital Hamiltonian operator and new Zeeman effect of two-dimensional system are investigated. We have shown that, the new energy of diatomic molecule is the sum of ordinary energy of modified Kratzer-type potential, in commutative space, and new additive terms due to the contribution of the additive part of the NMKP. We have shown also that, the group symmetry of (NC: 2D-RSP) reduce to new sub-group symmetry of NC two-dimensional real space (NC: 2D-RSP) under new modified Kratzer-type interactions.

Info:

Periodical:
International Letters of Chemistry, Physics and Astronomy (Volume 76)
Pages:
1-11
Citation:
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, pp. 1-11, 2017
Online since:
October 2017
Export:
Distribution:
References:

[1] 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

[2] 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(9) (2015) 2018–(2027).

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

[3] 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

[4] D. Agboola, Complete analytical solutions of the Mie-type potentials in n-dimensions, Acta Physica Polonica A. 120(3) (2011) 371–377.

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

[5] C. Berkdemir, A. Berkdemir, J. Han, Bound state solutions of the Schrödinger equation for modified Kreutzer's molecular potential, Chemical Physics Letters. 417(4) (2006) 326–329.

DOI: https://doi.org/10.1016/j.cplett.2005.10.039

[6] S. Erkoc, R. Sever, Path-integral solution for a Mie-type potential, Phys. Rev. D. 30(10) (1984) 2117.

DOI: https://doi.org/10.1103/physrevd.30.2117

[7] J. Sadeghia, B. Pourhassan, Exact solution of the non-central modified Kratzer potential plus a ring-shaped like potential by the factorization method, Electronic Journal of Theoretical Physics. 5(17) (2008) 197-206.

[8] S.M. Ikhdair, R. Sever, Exact quantization rule to the Kratzer-type potentials: an application to the diatomic molecules, J. Math. Chem. 45 (2009) 1137–1152.

DOI: https://doi.org/10.1007/s10910-008-9438-8

[9] A. Connes, M.R. Douglas, A. Schwarz, Noncommutative geometry and matrix theory, Journal of High Energy Physics. 1998(02) (1998) 003.

DOI: https://doi.org/10.1088/1126-6708/1998/02/003

[10] A.E.F. Djemei, H. Smail, On quantum mechanics on noncommutative quantum phase space, Commun. Theor. Phys. 41(6) (2004) 837-844.

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

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

[12] 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

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

[14] J. Mamat, S. Dulat, H. Mamatabdulla, Landau-like atomic problem on a non-commutative phase space, Int. J. Theor. Phys. 55(6) (2016) 2913-2918.

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

[15] F. Hoseini, J.K. Saha, H. Hassanabadi, Investigation of fermions in non-commutative space by considering Kratzer potential, Commun. Theor. Phys. 65(6) (2016) 695-700.

DOI: https://doi.org/10.1088/0253-6102/65/6/695

[16] K.H.C. Castello-Branco, A.G. Martins, Free-fall in a uniform gravitational field in noncommutative quantum mechanics, Journal of Mathematical Physics. 51(10) (2010) 102106.

DOI: https://doi.org/10.1063/1.3466812

[17] O. Bertolami, P. Leal, Aspects of phase-space noncommutative quantum mechanics, Physics Letters B. 750 (2015) 6–11.

DOI: https://doi.org/10.1016/j.physletb.2015.08.024

[18] C. Bastos et al., Weyl–Wigner formulation of noncommutative quantum mechanics, J. Math. Phys. 49(7) (2008) 072101.

[19] J.Z. Zhang, Fractional angular momentum in non-commutative spaces, Physics Letters B. 584(1-2) (2004) 204–209.

DOI: https://doi.org/10.1016/j.physletb.2004.01.049

[20] V.P. Nair, A.P. Polychronakos, Quantum mechanics on the noncommutative plane and sphere, Physics Letters B. 505(1–4) (2001) 267-274.

DOI: https://doi.org/10.1016/s0370-2693(01)00339-2

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

[22] F.G. Scholtz et al., Dual families of noncommutative quantum systems, Phys. Rev. D. 71(8) (2005) 085005.

[23] M. Chaichian, M.M. Sheikh-Jabbari, A. Tureanu, Hydrogen atom spectrum and the Lamb shift in noncommutative QED, Phys. Rev. Lett. 86(13) (2001) 2716.

DOI: https://doi.org/10.1103/physrevlett.86.2716

[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, 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

[26] 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. 73 (2017) 31-45.

DOI: https://doi.org/10.18052/www.scipress.com/ilcpa.73.31

[27] A. Maireche, Investigations on the relativistic interactions in one-electron atoms with modified Yukawa potential for spin 1/2 particles, International Frontier Science Letters. 11 (2017) 29-44.

DOI: https://doi.org/10.18052/www.scipress.com/ifsl.11.29

[28] 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.

[29] 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(4) (2015) 03047-1–03047-7.

[30] 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

[31] A. Maireche, A new theoretical study of quantum atomic energy spectra for lowest excited states of central (PIHOIQ) potential in noncommutative spaces and phases symmetries at Plank's and nanoscales, J. Nano- Electron. Phys. 8(1) (2016).

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

[32] 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

[33] 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.

DOI: https://doi.org/10.21272/jnep.8(4(1)).04027

[34] A. Maireche, A new nonrelativistic investigation for interactions in one-electron atoms with modified vibrational-rotational analysis of supersingular plus quadratic potential: extended quantum mechanics, J. Nano- Electron. Phys. 8(4) (2016).

DOI: https://doi.org/10.21272/jnep.8(4(2)).04076

[35] A. Maireche, Investigations on the relativistic interactions in one-electron atoms with modified anharmonic oscillator, J. Nanomed. Res. 4(4) (2016) 00097.

DOI: https://doi.org/10.15406/jnmr.2016.04.00097

[36] A. Maireche, A new nonrelativistic investigation for interactions in one-electron atoms with modified inverse-square potential: noncommutative two and three dimensional space phase solutions at Planck's and nano-scales. J Nanomed. Res 4(3) (2016).

DOI: https://doi.org/10.15406/jnmr.2016.04.00090

[37] 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.

[38] 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

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

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

[42] 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.

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

[44] 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.

[45] 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.

[46] A. Maireche, New exact energy eigenvalues for (MIQYH) and (MIQHM) central potentials: non-relativistic solutions, Afr. Rev Phys. 11 (2016) 175-184.

[47] A. Maireche, The exact nonrelativistic energy eigenvalues for modified inversely quadratic Yukawa potential plus Mie-type potential, J. Nano- Electron. Phys. 9(2) (2017) 02017-1–02017-7.

DOI: https://doi.org/10.21272/jnep.9(2).02017

[48] A. Maireche, Deformed energy levels of a pseudoharmonic potential: nonrelativistic quantum mechanics, Yanbu Journal of Engineering and Science. 12 (2016) 55-63.

[49] M. Abramowitz, I.A. Stegun, Handbook of mathematical functions with formulas, Graphs and Mathematical Tables, Dover Publications, New York, (1965).

DOI: https://doi.org/10.2307/1266136
Show More Hide
Cited By:

[1] 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

[2] B. Ita, H. Louis, E. Ubana, P. Ekuri, C. Leonard, N. Nzeata, "Evaluation of the bound state energies of some diatomic molecules from the approximate solutions of the Schrodinger equation with Eckart plus inversely quadratic Yukawa potential", Journal of Molecular Modeling, Vol. 26, 2020

DOI: https://doi.org/10.1007/s00894-020-04593-0