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Advances in High Energy Physics
Volume 2016 (2016), Article ID 3647392, 5 pages
http://dx.doi.org/10.1155/2016/3647392
Research Article

Study of Time Evolution for Approximation of Two-Body Spinless Salpeter Equation in Presence of Time-Dependent Interaction

Physics Department, Shahrood University of Technology, P.O. Box 3619995161-316, Shahrood, Iran

Received 20 December 2015; Revised 31 January 2016; Accepted 17 February 2016

Academic Editor: Ming Liu

Copyright © 2016 Hadi Sobhani and Hassan Hassanabadi. 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. E. E. Salpeter and H. A. Bethe, “A relativistic equation for bound-state problems,” Physical Review, vol. 84, no. 6, pp. 1232–1242, 1951. View at Publisher · View at Google Scholar
  2. G. C. Wick, “Properties of Bethe-Salpeter wave functions,” Physical Review Letters, vol. 96, pp. 1124–1134, 1954. View at Google Scholar · View at MathSciNet
  3. R. E. Cutkosky, “Solutions of a bethe-salpeter equation,” Physical Review Letters, vol. 96, no. 4, article 1135, 1954. View at Publisher · View at Google Scholar
  4. G. Wanders, “Limite non-relativiste d'une équation de Bethe-Salpeter,” Helvetica Physica Acta, vol. 30, no. 5, p. 417, 1957. View at Publisher · View at Google Scholar
  5. M. Ida and K. Maki, “On vertical representation of Bethe-Salpeter amplitudes,” Progress of Theoretical Physics, vol. 26, pp. 470–482, 1961. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. I. Sato, “Normalization condition for the BEThe-SALpeter wavefunction and a formal solution to the BEThe-SALpeter equation,” Journal of Mathematical Physics, vol. 4, pp. 24–35, 1963. View at Publisher · View at Google Scholar · View at MathSciNet
  7. S. Hassanabadi, M. Ghominejad, S. Zarrinkamar, and H. Hassanabadi, “The Yukawa potential in semirelativistic formulation via supersymmetry quantum mechanics,” Chinese Physics B, vol. 22, no. 6, Article ID 060303, 2013. View at Google Scholar
  8. W. Lucha and F. F. Schöberl, “Variational approach to the spinless relativistic Coulomb problem,” Physical Review C, vol. 50, no. 8, pp. 5443–5445, 1994. View at Publisher · View at Google Scholar
  9. D. Jacquemin, I. Duchemin, and X. Blase, “Benchmarking the Bethe-Salpeter formalism on a standard organic molecular set,” Journal of Chemical Theory and Computation, vol. 11, no. 7, pp. 3290–3304, 2015. View at Publisher · View at Google Scholar
  10. G. B. Mainland, “Using analytical solutions at large momentum transfer to obtain zero-energy, bound-state, Bethe–Salpeter solutions of a scalar and spin-1/2 fermion exchanging photons,” Few-Body Systems, vol. 56, no. 4, pp. 197–218, 2015. View at Publisher · View at Google Scholar
  11. G. Eichmann, Ch. S. Fischer, and W. Heupel, “Tetraquarks from the Bethe-Salpeter equation,” Acta Physica Polonica B: Proceedings Supplement, vol. 8, no. 1, p. 425, 2015. View at Publisher · View at Google Scholar
  12. M. Shao, F. H. da Jornada, C. Yang, J. Deslippe, and S. G. Louie, “Structure preserving parallel algorithms for solving the Bethe-Salpeter eigenvalue problem,” Linear Algebra and Its Applications, vol. 488, pp. 148–167, 2016. View at Publisher · View at Google Scholar
  13. G. Mishima, R. Jinno, and T. Kitahara, “Diquark bound states with a completely crossed ladder truncation,” Physical Review D, vol. 91, no. 7, Article ID 076011, 2015. View at Publisher · View at Google Scholar
  14. D. Owen and R. Barrett, “Application of the Bethe-Salpeter equation to mesonic atoms,” http://arxiv.org/abs/1505.06809.
  15. J. Carbonell and V. A. Karmanov, “Transition electromagnetic form factor and current conservation in the Bethe-Salpeter approach,” Physical Review D, vol. 91, no. 7, Article ID 076010, 2015. View at Publisher · View at Google Scholar
  16. H. Hassanabadi, S. Zarrinkamar, and B. H. Yazarloo, “Spectrum of a hyperbolic potential via SUSYQM within the semi-relativistic for- malism,” Chinese Journal of Physics, vol. 50, p. 5, 2012. View at Google Scholar
  17. S. Hassanabadi, M. Ghominejad, S. Zarrinkamar, and H. Hassanabadi, “The Yukawa potential in semirelativistic formulation via supersymmetry quantum mechanics,” Chinese Physics B, vol. 22, no. 6, Article ID 060303, 2013. View at Publisher · View at Google Scholar
  18. S. Hassanabadi, M. Ghominejad, B. H. Yazarloo, S. Zarrinkamar, and H. Hassanabadi, “Two-body Spinless Salpeter equation for the Woods-Saxon potential,” Chinese Physics C, vol. 37, no. 8, Article ID 083102, 2013. View at Publisher · View at Google Scholar
  19. S. Zarrinkamar, A. A. Rajabi, B. H. Yazarloo, and H. Hassanabadi, “The soft-core coulomb potential in the semi-relativistic two-body basis,” Few-Body Systems, vol. 54, no. 11, pp. 2001–2007, 2013. View at Publisher · View at Google Scholar · View at Scopus
  20. H. G. Oh, H. R. Lee, T. F. George, and C. I. Um, “Exact wave functions and coherent states of a damped driven harmonic oscillator,” Physical Review A, vol. 39, no. 11, pp. 5515–5522, 1989. View at Publisher · View at Google Scholar
  21. M. Maamache and H. Choutri, “Exact evolution of the generalized damped harmonic oscillator,” Journal of Physics A: Mathematical and General, vol. 33, no. 35, pp. 6203–6210, 2000. View at Publisher · View at Google Scholar · View at Scopus
  22. H. R. Lewis Jr. and W. B. Riesenfeld, “An exact quantum theory of the timedependent harmonic oscillator and of a charged particle in a timedependent electromagnetic field,” Journal of Mathematical Physics, vol. 10, no. 8, pp. 1458–1473, 1969. View at Publisher · View at Google Scholar
  23. I. Guedes, “Reply to: Comment on ‘Solution of the Schrödinger equation for the time-dependent linear potential’,” Physical Review A, vol. 68, no. 1, Article ID 016102, 2003. View at Publisher · View at Google Scholar
  24. E. J. Heller, “Wavepacket path integral formulation of semiclassical dynamics,” Chemical Physics Letters, vol. 34, no. 2, pp. 321–325, 1975. View at Publisher · View at Google Scholar
  25. S. Albeverio and S. Mazzucchi, “The time-dependent quartic oscillator—a Feynman path integral approach,” Journal of Functional Analysis, vol. 238, no. 2, pp. 471–488, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  26. V. G. Ibarra-Sierra, J. C. Sandoval-Santana, J. L. Cardoso, and A. Kunold, “Lie algebraic approach to the time-dependent quantum general harmonic oscillator and the bi-dimensional charged particle in time-dependent electromagnetic fields,” Annals of Physics, vol. 362, pp. 83–117, 2015. View at Publisher · View at Google Scholar
  27. A. L. de Lima, A. Rosas, and I. A. Pedrosa, “On the quantum motion of a generalized time-dependent forced harmonic oscillator,” Annals of Physics, vol. 323, no. 9, pp. 2253–2264, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  28. J. R. Choi, “Exact wave functions of time-dependent Hamiltonian systems involving quadratic, inverse quadratic, and 1/x^p^+p^1/x^ terms,” International Journal of Theoretical Physics, vol. 42, no. 4, pp. 853–861, 2003. View at Publisher · View at Google Scholar
  29. I. A. Pedrosa, A. L. de Lima, and A. M. D. M. Carvalho, “Gaussian wave packet states of a generalized inverted harmonic oscillator with time-dependent mass and frequency,” Canadian Journal of Physics, vol. 93, no. 8, pp. 841–845, 2015. View at Publisher · View at Google Scholar
  30. S. Menouar, M. Maamacheand, and J. R. Choi, “Gaussian wave packet for a time-dependent harmonic oscillator model of a charged particle in a variable magnetic field,” Chinese Journal of Physics, vol. 49, no. 4, pp. 871–876, 2011. View at Google Scholar
  31. S. Menouar, M. Maamache, H. Bekkar, and J. R. Choi, “Gaussian wave packet for time-dependent Hamiltonian systems involving quadratic, inverse quadratic, and 1/xp+p1/x Terms,” Journal of the Korean Physical Society, vol. 58, no. 1, pp. 154–157, 2011. View at Publisher · View at Google Scholar
  32. J. Wei and E. Norman, “Lie algebraic solution of linear differential equations,” Journal of Mathematical Physics, vol. 4, pp. 575–581, 1963. View at Publisher · View at Google Scholar · View at MathSciNet