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Year 2018, Volume 5, Issue 2, 97 - 103, 29.06.2018
https://doi.org/10.17350/HJSE19030000079

Abstract

References

  • 1. Greiner, W. Relativistic Quantum Mechanics, third ed. Springer, Berlin, 2000.
  • 2. Landau, L. D., Lifshitz, E. M. Quantum Mechanics NonRelativistic Theory, second ed. Pergamon, London, 1965.
  • 3. Buyukkilic, F., Egrifes, H., Demirhan, D. Solution of the Schrödinger equation for two different molecular potentials by the Nikiforov-Uvarov method. Theor. Chem. Acc. 98 (1997) 192-196.
  • 4. Yang, Q. B. Deformed Symmetrical Double-well Potential. Acta. Photon. Sin. 32 (2003) 882-884.
  • 5. Arai, A. Exactly solvable supersymmetric quantum mechanics. J. Math. Anal. Appl. 158 (1991) 63-79.
  • 6. Zhao, X. Q., Jia, C. S., Yang, Q. B. Bound states of relativistic particles in the generalized symmetrical double-well potential. Phys. Lett. A 337 (2005) 189-196.
  • 7. Wei, G. F., Chen, W. L. Arbitrary l-wave bound states of the Schrödinger equation for the hyperbolical molecular potential. Int. J. Quantum Chem. 114 (2014), 1602-1606.
  • 8. Wei, G. F., Chen, W. L., Dong, S. H. The arbitrary l continuum states of the hyperbolic molecular potential. Phys. Lett. A 378 (2014) 2367-2370.
  • 9. Candemir, N. Klein–Gordon particles in symmetrical well potential. Appl. Math. Comput. 274 (2016) 531–538.
  • 10. Nikiforov, A.F., Uvarov, V.B. Special functions of mathematical physics: a unified introduction with applications, first ed. Birkhäuser, 1988.
  • 11. Greene, R.L., Aldrich, C. Variational wave functions for a screened Coulomb potential. Phys. Rev. A 14 (1976) 2363– 2366.
  • 12. Ciftci, H., Hall, R.L., Saad, N. Asymptotic iteration method for eigenvalue problems. J. Phys. A: Math. Gen. 36 (2003) 11807–11816.
  • 13. Ciftci, H., Hall, R.L., Saad, N. Perturbation theory in a framework of iteration methods. Phys. Lett. A 340 (2005) 388–396.
  • 14. Ciftci, H., Hall, R.L., Saad, N. Exact and approximate solutions of Schrödinger's equation for a class of trigonometric potentials. Centr. Eur. J. Phys. 11 (2013) 37–48.
  • 15. Ikhdair, S.M. An improved approximation scheme for the centrifugal term and the Hulthén potential. Eur. Phys. J. A 39 (2009) 307–314.
  • 16. Aydogdu, O., Yanar, H. Bound and scattering states for a hyperbolic-type potential in view of a new developed approximation. Int. J. Quantum Chem. 115 (2015) 529–534.
  • 17. Alhaidari, A.D., Bahlouli, H., Al-Hasan, A. Dirac and Klein– Gordon equations with equal scalar and vector potentials. Phys. Lett. A 349 (2006) 87–97.
  • 18. Yasuk, F., Durmus, A., Boztosun, I. Exact analytical solution to the relativistic Klein–Gordon equation with noncentral equal scalar and vector potentials. J. Math. Phys. 47 (2006) 082302.
  • 19. Ciftci, H., Hall, R.L., Saad, N. Construction of exact solutions to eigenvalue problems by the asymptotic iteration method. J. Phys. A: Math. Gen. 38 (2005) 1147–1156.
  • 20. Ol ar, E., Koç, R., Tütüncüler, H. The exact solution of the s-wave Klein–Gordon equation for the generalized Hulthén potential by the asymptotic iteration method. Phys. Scr. 78 (2008) 015011.
  • 21. Alsadi, K.S. Exact Solutions of Dirac-Rosen-Morse Problem via Asymptotic Iteration Method. J. Nanoelectron. Optoe. 10 (2015) 683–687.
  • 22. Hall, R.L., Saad, N. Schrödinger spectrum generated by the Cornell potential. Open Phys. 13 (2015) 83–89.
  • 23. Fernandez, F.M. On an iteration method for eigenvalue problems. J. Phys. A: Math. Gen. 37 (2004) 6173–6180.
  • 24. Barakat, T., Al-Dossary, O.M. The Asymptotic Iteration Method For The Eigenenergies Of The Asymmetrical Quantum Anharmonic Oscillator Potentials. Int. J. Mod. Phys. A 22 (2007) 203–212.
  • 25. Nieto, M. M. Hydrogen atom and relativistic pi–mesic atom in N-space dimensions. Am. J. Phys. 47 (1979) 1067–1072.
  • 26. Avery, J. Hyperspherical Harmonics: Applications in Quantum Theory, first ed. Kluwer Academic Publishers, 1989.
  • 27. Cavalli, S., Aquilanti, V., Grossi, G. Hyperspherical coordinates for molecular dynamics by the method of trees and the mapping of potential energy surfaces for triatomic systems. J. Chem. Phys. 85 (1986) 1362–1375.
  • 28. Nouri, S. Generalized coherent states for the d-dimensional Coulomb problem. Phys. Rev. A 60 (1999) 1702–1705.
  • 29. Avery, J. Hyperspherical Harmonics and Generalized Sturmians, first ed. Kluwer Academic Publishers, 2002.
  • 30. Diaz, R., Pariguan, E. On hypergeometric functions and Pochhammer k-symbol. Divulg. Mat. 15 (2007) 179–192.
  • 31. Mubeen, S., Rehman, A. A Note on k-Gamma Function and Pochhammer k-Symbol. Journal of Informatics and Mathematical Sciences 6 (2014) 93–107.
  • 32. Ciftci, H., Kisoglu, H.F. Application of asymptotic iteration method to a deformed well problem. Chinese Phys. B 25 (2016) 030201.
  • 33. Kisoglu, H.F., Ciftci, H. Accidental Degeneracies in N dimensions for Potential Class via Asymptotic Iteration Method (AIM). Commun. Theor. Phys. 67 (2017) 350–354.
  • 34. Kiriushcheva, N., Kuzmin, S. Scattering of a Gaussian wave packet by a reflectionless potential. Am. J. Phys 66 (1998) 867–872.
  • 35. Qiang, W.-C. Bound states of the Klein–Gordon and Dirac equations for potential . Chin. Phys. 13 (2004) 571.

N-Dimensional Solutions of Klein-Gordon Particles for Scaled Molecular Potential via Highly-Accurate Approximation

Year 2018, Volume 5, Issue 2, 97 - 103, 29.06.2018
https://doi.org/10.17350/HJSE19030000079

Abstract

The energy eigenvalues and eigenfunctions of relativistic scalar particles are obtained for an equal vector and scalar symmetrical molecular potential in N-dimensional euclidean space by using Asymptotic Iteration Method. For such a calculation, the potential in the eigenvalue equation is scaled regarding to fact that the potential is the same in non-relativistic limit. Furthermore, an highly-accurate approximation scheme is used to deal with the centrifugal term in the eigenvalue equation. The results obtained are compared with the ones that exist in literature.

References

  • 1. Greiner, W. Relativistic Quantum Mechanics, third ed. Springer, Berlin, 2000.
  • 2. Landau, L. D., Lifshitz, E. M. Quantum Mechanics NonRelativistic Theory, second ed. Pergamon, London, 1965.
  • 3. Buyukkilic, F., Egrifes, H., Demirhan, D. Solution of the Schrödinger equation for two different molecular potentials by the Nikiforov-Uvarov method. Theor. Chem. Acc. 98 (1997) 192-196.
  • 4. Yang, Q. B. Deformed Symmetrical Double-well Potential. Acta. Photon. Sin. 32 (2003) 882-884.
  • 5. Arai, A. Exactly solvable supersymmetric quantum mechanics. J. Math. Anal. Appl. 158 (1991) 63-79.
  • 6. Zhao, X. Q., Jia, C. S., Yang, Q. B. Bound states of relativistic particles in the generalized symmetrical double-well potential. Phys. Lett. A 337 (2005) 189-196.
  • 7. Wei, G. F., Chen, W. L. Arbitrary l-wave bound states of the Schrödinger equation for the hyperbolical molecular potential. Int. J. Quantum Chem. 114 (2014), 1602-1606.
  • 8. Wei, G. F., Chen, W. L., Dong, S. H. The arbitrary l continuum states of the hyperbolic molecular potential. Phys. Lett. A 378 (2014) 2367-2370.
  • 9. Candemir, N. Klein–Gordon particles in symmetrical well potential. Appl. Math. Comput. 274 (2016) 531–538.
  • 10. Nikiforov, A.F., Uvarov, V.B. Special functions of mathematical physics: a unified introduction with applications, first ed. Birkhäuser, 1988.
  • 11. Greene, R.L., Aldrich, C. Variational wave functions for a screened Coulomb potential. Phys. Rev. A 14 (1976) 2363– 2366.
  • 12. Ciftci, H., Hall, R.L., Saad, N. Asymptotic iteration method for eigenvalue problems. J. Phys. A: Math. Gen. 36 (2003) 11807–11816.
  • 13. Ciftci, H., Hall, R.L., Saad, N. Perturbation theory in a framework of iteration methods. Phys. Lett. A 340 (2005) 388–396.
  • 14. Ciftci, H., Hall, R.L., Saad, N. Exact and approximate solutions of Schrödinger's equation for a class of trigonometric potentials. Centr. Eur. J. Phys. 11 (2013) 37–48.
  • 15. Ikhdair, S.M. An improved approximation scheme for the centrifugal term and the Hulthén potential. Eur. Phys. J. A 39 (2009) 307–314.
  • 16. Aydogdu, O., Yanar, H. Bound and scattering states for a hyperbolic-type potential in view of a new developed approximation. Int. J. Quantum Chem. 115 (2015) 529–534.
  • 17. Alhaidari, A.D., Bahlouli, H., Al-Hasan, A. Dirac and Klein– Gordon equations with equal scalar and vector potentials. Phys. Lett. A 349 (2006) 87–97.
  • 18. Yasuk, F., Durmus, A., Boztosun, I. Exact analytical solution to the relativistic Klein–Gordon equation with noncentral equal scalar and vector potentials. J. Math. Phys. 47 (2006) 082302.
  • 19. Ciftci, H., Hall, R.L., Saad, N. Construction of exact solutions to eigenvalue problems by the asymptotic iteration method. J. Phys. A: Math. Gen. 38 (2005) 1147–1156.
  • 20. Ol ar, E., Koç, R., Tütüncüler, H. The exact solution of the s-wave Klein–Gordon equation for the generalized Hulthén potential by the asymptotic iteration method. Phys. Scr. 78 (2008) 015011.
  • 21. Alsadi, K.S. Exact Solutions of Dirac-Rosen-Morse Problem via Asymptotic Iteration Method. J. Nanoelectron. Optoe. 10 (2015) 683–687.
  • 22. Hall, R.L., Saad, N. Schrödinger spectrum generated by the Cornell potential. Open Phys. 13 (2015) 83–89.
  • 23. Fernandez, F.M. On an iteration method for eigenvalue problems. J. Phys. A: Math. Gen. 37 (2004) 6173–6180.
  • 24. Barakat, T., Al-Dossary, O.M. The Asymptotic Iteration Method For The Eigenenergies Of The Asymmetrical Quantum Anharmonic Oscillator Potentials. Int. J. Mod. Phys. A 22 (2007) 203–212.
  • 25. Nieto, M. M. Hydrogen atom and relativistic pi–mesic atom in N-space dimensions. Am. J. Phys. 47 (1979) 1067–1072.
  • 26. Avery, J. Hyperspherical Harmonics: Applications in Quantum Theory, first ed. Kluwer Academic Publishers, 1989.
  • 27. Cavalli, S., Aquilanti, V., Grossi, G. Hyperspherical coordinates for molecular dynamics by the method of trees and the mapping of potential energy surfaces for triatomic systems. J. Chem. Phys. 85 (1986) 1362–1375.
  • 28. Nouri, S. Generalized coherent states for the d-dimensional Coulomb problem. Phys. Rev. A 60 (1999) 1702–1705.
  • 29. Avery, J. Hyperspherical Harmonics and Generalized Sturmians, first ed. Kluwer Academic Publishers, 2002.
  • 30. Diaz, R., Pariguan, E. On hypergeometric functions and Pochhammer k-symbol. Divulg. Mat. 15 (2007) 179–192.
  • 31. Mubeen, S., Rehman, A. A Note on k-Gamma Function and Pochhammer k-Symbol. Journal of Informatics and Mathematical Sciences 6 (2014) 93–107.
  • 32. Ciftci, H., Kisoglu, H.F. Application of asymptotic iteration method to a deformed well problem. Chinese Phys. B 25 (2016) 030201.
  • 33. Kisoglu, H.F., Ciftci, H. Accidental Degeneracies in N dimensions for Potential Class via Asymptotic Iteration Method (AIM). Commun. Theor. Phys. 67 (2017) 350–354.
  • 34. Kiriushcheva, N., Kuzmin, S. Scattering of a Gaussian wave packet by a reflectionless potential. Am. J. Phys 66 (1998) 867–872.
  • 35. Qiang, W.-C. Bound states of the Klein–Gordon and Dirac equations for potential . Chin. Phys. 13 (2004) 571.

Details

Primary Language English
Journal Section Research Article
Authors

Hasan Fatih KİSOGLU This is me
Mersin University, Department of Basic Sciences, Mersin, Turkey

Publication Date June 29, 2018
Application Date
Acceptance Date
Published in Issue Year 2018, Volume 5, Issue 2

Cite

Bibtex @ { hjse859940, journal = {Hittite Journal of Science and Engineering}, eissn = {2148-4171}, address = {Hitit Üniversitesi Mühendislik Fakültesi Kuzey Kampüsü Çevre Yolu Bulvarı 19030 Çorum / TÜRKİYE}, publisher = {Hitit University}, year = {2018}, volume = {5}, number = {2}, pages = {97 - 103}, doi = {10.17350/HJSE19030000079}, title = {N-Dimensional Solutions of Klein-Gordon Particles for Scaled Molecular Potential via Highly-Accurate Approximation}, key = {cite}, author = {Kisoglu, Hasan Fatih} }
APA Kisoglu, H. F. (2018). N-Dimensional Solutions of Klein-Gordon Particles for Scaled Molecular Potential via Highly-Accurate Approximation . Hittite Journal of Science and Engineering , 5 (2) , 97-103 . DOI: 10.17350/HJSE19030000079
MLA Kisoglu, H. F. "N-Dimensional Solutions of Klein-Gordon Particles for Scaled Molecular Potential via Highly-Accurate Approximation" . Hittite Journal of Science and Engineering 5 (2018 ): 97-103 <https://dergipark.org.tr/en/pub/hjse/issue/59663/859940>
Chicago Kisoglu, H. F. "N-Dimensional Solutions of Klein-Gordon Particles for Scaled Molecular Potential via Highly-Accurate Approximation". Hittite Journal of Science and Engineering 5 (2018 ): 97-103
RIS TY - JOUR T1 - N-Dimensional Solutions of Klein-Gordon Particles for Scaled Molecular Potential via Highly-Accurate Approximation AU - Hasan FatihKisoglu Y1 - 2018 PY - 2018 N1 - doi: 10.17350/HJSE19030000079 DO - 10.17350/HJSE19030000079 T2 - Hittite Journal of Science and Engineering JF - Journal JO - JOR SP - 97 EP - 103 VL - 5 IS - 2 SN - -2148-4171 M3 - doi: 10.17350/HJSE19030000079 UR - https://doi.org/10.17350/HJSE19030000079 Y2 - 2022 ER -
EndNote %0 Hittite Journal of Science and Engineering N-Dimensional Solutions of Klein-Gordon Particles for Scaled Molecular Potential via Highly-Accurate Approximation %A Hasan Fatih Kisoglu %T N-Dimensional Solutions of Klein-Gordon Particles for Scaled Molecular Potential via Highly-Accurate Approximation %D 2018 %J Hittite Journal of Science and Engineering %P -2148-4171 %V 5 %N 2 %R doi: 10.17350/HJSE19030000079 %U 10.17350/HJSE19030000079
ISNAD Kisoglu, Hasan Fatih . "N-Dimensional Solutions of Klein-Gordon Particles for Scaled Molecular Potential via Highly-Accurate Approximation". Hittite Journal of Science and Engineering 5 / 2 (June 2018): 97-103 . https://doi.org/10.17350/HJSE19030000079
AMA Kisoglu H. F. N-Dimensional Solutions of Klein-Gordon Particles for Scaled Molecular Potential via Highly-Accurate Approximation. Hittite J Sci Eng. 2018; 5(2): 97-103.
Vancouver Kisoglu H. F. N-Dimensional Solutions of Klein-Gordon Particles for Scaled Molecular Potential via Highly-Accurate Approximation. Hittite Journal of Science and Engineering. 2018; 5(2): 97-103.
IEEE H. F. Kisoglu , "N-Dimensional Solutions of Klein-Gordon Particles for Scaled Molecular Potential via Highly-Accurate Approximation", Hittite Journal of Science and Engineering, vol. 5, no. 2, pp. 97-103, Jun. 2018, doi:10.17350/HJSE19030000079