Analytical solution of the Duffin - Kemmer - Petiau equation for the sum of the Manning - Rosen and the Yukawa class potential
This paper presents an analytical bound-state solution to the Duffin - Kemmer - Petiau equation for the new putative combined Manning - Rosen and Yukawa class potentials. Using the developed scheme to approximate and overcome the difficulties arising in the centrifugal part of the potential, the bound-state solution of the modified Duffin - Kemmer - Petiau equation is found. Analytical expressions of energy eigenvalue and the corresponding radial wave functions are obtained for an arbitrary value of the orbital quantum number l . Also, eigenfunctions are expressed in terms of hypergeometric functions. It is shown that energy levels and eigenfunctions are quite sensitive to the choice of radial and orbital quantum numbers.
Download file
Counter downloads: 38
Keywords
Manning - Rosen plus Yukawa class potential, Nikiforov - Uvarov method, spectral problemAuthors
| Name | Organization | |
| Aslanova S.M. | Baku State University | sariyya.aslanova@mail.ru |
References
Greiner W. Relativistic Quantum Mechanics. - 3ed. edition. - Berlin: Springer, 2000.
Bagrov V.G. and Gitman D.M. Exact Solutions of Relativistic Wave Equations. - Dordrecht: Kluwer Academic Publishers, 1990.
Nedjadi Y. and Barrett R.C. // J. Phys. G. - 1993. - V. 19. - P. 87.
Krajcik R.A. and Nieto M.M. // Am. J. Phys. - 1977. - V. 45. - P. 818.
Dirac P.A.M. // Proc. R. Soc. London. Ser. A. - 1936. - V. 155. - P. 447.
Petiau G. University of Paris: Thesis. - Published in Acad. Roy. Belg. Classe Sci. Mem. Collect., 1936. - No. 16(2). - P. 8.
Duffin R.J. // Phys. Rev. 1938. - V. 54. - P. 1114.
Kemmer N. // Proc. Roy. Soc. A. - 1939. - V. 173. - P. 91.
Boutabia-Cheraitia B. and Boudjedaa T. // Phys. Lett. A. - 2005. - V. 338. - P. 97.
Hassanabadi H., Kamali M., and Yazarloo B.H. // Can. J. Phys. - 2014. - V. 92. - P. 465.
Yaşuk F., Berkdemir C., Berkdemir A., and and Önem C. // Phys. Scr. - 2005. - V. 71. - P. 340.
Багров В.Г., Мешков А.Г., Шаповалов В.Н., Шаповалов А.В. // Изв. вузов. Физика. - 1973. - T. 16. - № 11. - C. 66.
Багров В.Г., Мешков А.Г., Шаповалов В.Н., Шаповалов А.В. // Изв. вузов. Физика. - 1973. - T. 16. - № 12. - C. 45.
Багров В.Г., Мешков А.Г., Шаповалов В.Н., Шаповалов А.В. // Изв. вузов. Физика. - 1974. - T. 17. - № 6. - C. 74.
Багров В.Г., Мешков А.Г., Шаповалов В.Н., Шаповалов А.В. // Изв. вузов. Физика. - 1975. - T. 18. - № 3. - C. 152.
Ahmadov A.I., Demirci M., Aslanova S.M., and Mustamin M.F. // Phys. Lett. A. - 2020. - V. 384. - P. 126372.
Ahmadov A.I., Aslanova S.M., Orujova M.Sh., et al. // Phys. Lett. A. - 2019. - V. 383. - P. 3010.
Nagiyev Sh.M. and Ahmadov A.I. // Int. J. Mod. Phys. A. - 2019. - V. 34. - No. 17. - P. 1950089.
Ahmadov A.I., Nagiyev Sh.M., Qocayeva M.V., et al. // Int. J. Mod. Phys. A. - 2018. - V. 33. - P. 1850203.
Ahmadov A.I., Aydin C., and Uzun O. // Int. J. Mod. Phys. A. - 2014. - V. 29. - P. 1450002.
Nagiyev Sh.M., Ahmadov A.I., and Tarverdiyeva V.A. // Adv. High Energy Phys. - 2020. - V. 2020. - Art. ID 1356384.
Badalov V.H., Ahmadov H.I., and Badalov S.V. // Int. J. Mod. Phys. E. - 2010. - V. 19. - No. 07. - P. 1463.
Ahmadov A.I., Aslanova S.M., Orujova M.Sh., and Badalov S.V. // Adv. High Energy Phys. - 2021. - V. 2021. - Art. ID 8830063.
Nikiforov A.F. and Uvarov V.B. Special Functions of Mathematical Physics. - Basel: Birkhäuser, 1988.
Manning M.F. // Phys. Rev. - 1933. - V. 44. - P. 951.
Manning M.F. and Rosen N. // Phys. Rev. - 1933. - V. 44. - P. 953.
Yukawa H. // Proc. Phys. Math. Soc. Jpn. - 1935. - V. 17. - P. 48.
Qiang W.C. and Dong S.H. // Phys. Lett. A. - 2007. - V. 363. - P. 169.
Abramowitz M. and Stegun I.A. Handbook of Mathematical Functions with Formulas, Graphs, Mathematical Tables. - N.Y.: Dover, 1964.
Orudjev G.S. and Ismayilova N.A. // Adv. Phys. Res. - 2019. - V. 1. - No.1. - P. 37.
