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Advances in Mathematical Physics
Volume 2013 (2013), Article ID 258203, 10 pages
http://dx.doi.org/10.1155/2013/258203
Research Article
Wide Effectiveness of a Sine Basis for Quantum-Mechanical Problems in Dimensions
Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve Boulevard West, Montreal, QC, H3G 1M8, Canada
Received 24 October 2012; Accepted 18 December 2012
Academic Editor: D. E. Pelinovsky
Copyright © 2013 Richard L. Hall and Alexandra Lemus Rodríguez. 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.
Linked References
- K. Banerjee, S. P. Bhatnagar, V. Choudhry, and S. S. Kanwal, “The anharmonic oscillator,” Proceedings of the Royal Society A, vol. 360, no. 1703, pp. 575–586, 1978. View at Publisher · View at Google Scholar
- V. C. Aguilera-Navarro, E. Ley Koo, and A. H. Zimerman, “Perturbative, asymptotic and Padé-approximant solutions for harmonic and inverted oscillators in a box,” Journal of Physics A, vol. 13, no. 12, pp. 3585–3598, 1980. View at Publisher · View at Google Scholar · View at MathSciNet
- M. A. Shaqqor and S. M. AL-Jaber, “A confined hydrogen atom in higher space dimensions,” International Journal of Theoretical Physics, vol. 48, no. 8, pp. 2462–2472, 2009. View at Publisher · View at Google Scholar · View at Scopus
- H. E. Montgomery Jr., G. Campoy, and N. Aquino, “The confined N-dimensional harmonic oscillator revisited,” Physica Scripta, vol. 81, Article ID 045010, 2010. View at Publisher · View at Google Scholar
- R. L. Hall, N. Saad, and K. D. Sen, “Spectral characteristics for a spherically confined potential,” Journal of Physics. A, vol. 44, no. 18, Article ID 185307, 18 pages, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- A. Michels, J. De Boer, and A. Bijl, “Remarks concerning molecural interaction and their influence on the polarisability,” Physica, vol. 4, no. 10, pp. 981–994, 1937. View at Scopus
- Y. P. Varshni, “Critical cage radii for a confined hydrogen atom,” Journal of Physics B, vol. 31, no. 13, p. 2849, 1998. View at Publisher · View at Google Scholar
- S. M. Al-Jaber, “A confined -dimensional harmonic oscillator,” International Journal of Theoretical Physics, vol. 47, no. 7, pp. 1853–1864, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
- F. M. Fernández and E. A. Castro, “Hypervirial calculation of energy eigenvalues of a bounded centrally located harmonic oscillator,” Journal of Mathematical Physics, vol. 22, no. 8, pp. 1669–1671, 1981. View at Publisher · View at Google Scholar · View at MathSciNet
- H. Ciftci, R. L. Hall, and N. Saad, “Study of a confined hydrogen-like atom by the asymptotic iteration method,” International Journal of Quantum Chemistry, vol. 109, no. 5, pp. 931–937, 2009. View at Publisher · View at Google Scholar · View at Scopus
- X.-Y. Gu and J.-Q. Sun, “Any -state solutions of the Hulthén potential in arbitrary dimensions,” Journal of Mathematical Physics, vol. 51, no. 2, Article ID 022106, 6 pages, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
- D. Agboola, “Dirac equation with spin symmetry for the modified Pöschl-Teller potential in D dimensions,” Pramana, vol. 76, no. 6, pp. 875–885, 2011. View at Publisher · View at Google Scholar · View at Scopus
- M. Reed and B. Simon, Methods of Modern Mathematical Physics. IV. Analysis of Operators, Academic Press, New York, NY, USA, 1978. View at MathSciNet
- B. Simon, “Large orders and summability of eigenvalue perturbation theory: a mathematical overview,” International Journal of Quantum Chemistry, vol. 21, no. 1, pp. 3–5, 1992. View at Publisher · View at Google Scholar
- A. Sommerfeld, Partial Differential Equations in Physics, Academic Press, New York, NY, USA, 1949. View at MathSciNet
- R. L. Hall, Q. D. Katatbeh, and N. Saad, “A basis for variational calculations in dimensions,” Journal of Physics, vol. 37, no. 48, Article ID 11629, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- S.-H. Dong and Z.-Q. Ma, “Exact solutions to the Schrödinger equation for the potential in two dimensions,” Journal of Physics. A. Mathematical and General, vol. 31, no. 49, pp. 9855–9859, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- C.-S. Jia, J.-Y. Liu, Y. Sun, S. He, and L.-T. Sun, “A unified treatment of exactly solvable trigonometric potential models,” Physica Scripta, vol. 73, no. 2, pp. 164–168, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- H. Ciftci, R. L. Hall, and N. Saad, “Exact and approximate solutions of Schroedinger's equation for a class of trigonometric potentials,” Central European Journal of Physics, vol. 11, no. 1, pp. 37–48, 2013. View at Publisher · View at Google Scholar
- R. L. Hall, “Complementary pictures of the -boson problem,” Physical Review A, vol. 37, pp. 2673–2679, 1988. View at Publisher · View at Google Scholar
- R. L. Hall, “The ground-state energy of a system of identical bosons,” Journal of Mathematical Physics, vol. 29, no. 4, pp. 990–994, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- W. M. Houston, “A nuclear model,” Physical Review, vol. 47, no. 12, pp. 942–946, 1935. View at Publisher · View at Google Scholar
- H. R. Post, “Many-particle systems: derivation of a shell model,” Proceedings of the Physical Society, vol. 66, no. 7, p. 649, 1953. View at Publisher · View at Google Scholar
- J. B. McGuire, “Study of exactly soluble one-dimensional -body problems,” Journal of Mathematical Physics, vol. 5, pp. 622–636, 1964. View at Publisher · View at Google Scholar · View at MathSciNet
- D. C. Mattis, The Many-Body Problem: An Encyclopedia of Exactly Solved Models in One Dimension, World Scientific, Singapore, 2009. View at Publisher · View at Google Scholar · View at MathSciNet