Table of Contents Author Guidelines Submit a Manuscript
Advances in High Energy Physics
Volume 2017, Article ID 7937980, 19 pages
https://doi.org/10.1155/2017/7937980
Research Article

The Visualization of the Space Probability Distribution for a Moving Particle: In a Single Ring-Shaped Coulomb Potential

1New Energy and Electronic Engineering, Yancheng Teachers University, Yancheng 224002, China
2Laboratorio de Información Cuántica, CIDETEC, Instituto Politécnico Nacional, Unidad Profesional Adolfo López Mateos, 07700 Ciudad de México, Mexico

Correspondence should be addressed to Yuan You; moc.361@w_uoynauy, Chang-Yuan Chen; ten.361@yccctcy, and Shi-Hai Dong; moc.oohay@2hsgnod

Received 4 March 2017; Accepted 9 April 2017; Published 8 October 2017

Academic Editor: Saber Zarrinkamar

Copyright © 2017 Yuan You et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3.

Linked References

  1. C. Quesne, “A new ring-shaped potential and its dynamical invariance algebra,” Journal of Physics A.: Mathematical and General, vol. 21, no. 14, pp. 3093–3101, 1988. View at Publisher · View at Google Scholar · View at MathSciNet
  2. A. S. Zhedanov, “Hidden symmetry algebra and overlap coefficients for two ring-shaped potentials,” Journal of Physics A.: Mathematical and General, vol. 26, no. 18, pp. 4633–4641, 1993. View at Publisher · View at Google Scholar · View at MathSciNet
  3. C. Y. Chen and D. S. Sun, “Exact solutions of a ring-shaped oscillator,” Acta Photonica Sinica, vol. 30, p. 104, 2001. View at Google Scholar
  4. D. S. Sun and C. Y. Chen, “General formulas and recurrence formulas for radial matrix elements of ring shaped oscillator,” Acta Photonica Sinica, vol. 30, p. 539, 2001. View at Google Scholar
  5. S.-H. Dong, G.-H. Sun, and M. Lozada-Cassou, “An algebraic approach to the ring-shaped non-spherical oscillator,” Physics Letters. A, vol. 328, no. 4-5, pp. 299–305, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  6. J. Y. Guo, J. C. Han, and R. D. Wang, “Pseudospin symmetry and the relativistic ring-shaped non-spherical harmonic oscillator,” Physics Letters A, vol. 353, no. 5, pp. 378–382, 2006. View at Publisher · View at Google Scholar
  7. H. Hartmann, “The motion of a body in a ring-shaped potential,” Theoretica Chimica Acta, vol. 24, p. 201, 1972. View at Publisher · View at Google Scholar
  8. H. Hartmann and R. Schuck, “Spin-orbit coupling for the motion of a particle in a ring-shaped potential,” International Journal of Quantum Chemistry, vol. 18, p. 125, 1980. View at Publisher · View at Google Scholar
  9. B. P. Mandal, “Path integral solution of noncentral potential,” International Journal of Modern Physics A, vol. 15, no. 8, pp. 1225–1234, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
  10. G. G. Blado, “Supersymmetric treatment of a particle subjected to a ring-shaped potential,” International Journal of Quantum Chemistry, vol. 58, no. 5, pp. 431–439, 1996. View at Publisher · View at Google Scholar · View at Scopus
  11. C. C. Gerry, “Dynamical group for a ring potential,” Physics Letters A, vol. 118, no. 9, pp. 445–447, 1986. View at Publisher · View at Google Scholar · View at MathSciNet
  12. L. Chetouani, L. Guechi, and T. F. Hammann, “Algebraic treatment of a general noncentral potential,” Journal of Mathematical Physics, vol. 33, no. 10, pp. 3410–3418, 1992. View at Publisher · View at Google Scholar · View at MathSciNet
  13. C. Y. Chen, F. L. Lu, D. S. Sun, and S. H. Dong, “Analytic solutions of the double ring-shaped Coulomb potential in quantum mechanics,” Chinese Physical B, Article ID 100302, p. 22, 2013. View at Google Scholar
  14. C.-Y. Chen, D.-S. Sun, and C.-L. Liu, “The general calculation formulas and the recurrence relations of radial matrix elements for Hartmann potential,” Physics Letters A, vol. 317, pp. 80–86, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  15. H. Sobhani and H. Hassanabadi, “Davydov–chaban Hamiltonian in presence of time-dependent potential,” Physics Letters B, vol. 760, pp. 1–5, 2016. View at Publisher · View at Google Scholar · View at Scopus
  16. H. Hassanabadi, M. Kamali, Z. Molaee, and S. Zarrinkamar, “Duffin-Kemmer-Petiau equation under Hartmann ring-shaped potential,” Chinese Physics C, vol. 38, no. 3, Article ID 033102, 2014. View at Google Scholar
  17. M. Chabab, A. El Batoul, M. Oulne, H. Hassanabadi, and S. Zare, “Scattering states of the Schrödinger equation with a position-dependent-mass and a non-central potential,” Journal of the Korean Physical Society, vol. 69, no. 11, p. 1619, 2016. View at Publisher · View at Google Scholar
  18. S. Zarrinkamar, K. Jahankohan, and H. Hassanabadi, “The spin-orbit interaction in minimal length quantum mechanics; The case of a (2+1)- dimensional Dirac oscillator,” Canadian Journal of Physics, vol. 93, no. 12, pp. 1638–1641, 2015. View at Publisher · View at Google Scholar · View at Scopus
  19. A. N. Ikot, H. P. Obong, I. O. Owate, M. C. Onyeaju, and H. Hassanabadi, “Scattering state of klein-gordon particles by q-parameter hyperbolic poschl-teller potential,” Advances in High Energy Physics, Article ID 632603, 2015. View at Publisher · View at Google Scholar · View at Scopus
  20. W. Li, C. Y. Chen, and S. H. Dong, “Ring-shaped potential and a class of relevant integrals involved universal associated Legendre polynomials with complicated arguments,” Advances in High Energy Physics, Article ID 7374256, 2017. View at Google Scholar
  21. C. Y. Chen, F. L. Lu, D. S. Sun, Y. You, and S. H. Dong, “Exact solutions to a class of differential equation and some new mathematical properties for the universal associated-Legendre polynomials,” Applied Mathematics Letters, vol. 40, p. 90, 2015. View at Publisher · View at Google Scholar
  22. D. S. Sun, Y. You, F. L. Lu, C. Y. Chen, and S. H. Dong, “The quantum characteristics of a class of complicated double ring-shaped non-central potential,” Physica Scripta, vol. 89, Article ID 045002, 2014. View at Google Scholar
  23. R. Sari A, A. Suparmi, and C. Cari, “Exact solution of Dirac equation for Scarf potential with new tensor coupling potential for spin and pseudospin symmetries using Romanovski polynomials,” Chinese Physics B, vol. 25, Article ID 010301, 2016. View at Google Scholar
  24. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, Academic Press, Oxford, NY, USA, 6th edition, 2000. View at MathSciNet
  25. L. C. Andrews, Special Functions of Mathematics for Engineers, Oxford University Press, Oxford, NY, USA, 2nd edition, 1998. View at MathSciNet
  26. E. U. Condon and G. H. Shortley, The Theory of Atomic Spectra, Cambridge University press: Macmillan Company, NY, USA, 1935.
  27. P. Strange, Relativistic Quantum Mechanics, Oxford University Press, Oxford, NY, USA, 1998. View at Publisher · View at Google Scholar
  28. L. D. Landau and E. M. Lifshitz, Quantum Mechanics (Non-Relativistic Theory, Pergamon Press, Oxford, NY, USA, 3rd edition, 1977.