- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Advances in Mathematical Physics
Volume 2013 (2013), Article ID 258203, 10 pages
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, Canada H3G 1M8
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.
- 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.
- 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.
- 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.
- H. E. Montgomery Jr., G. Campoy, and N. Aquino, “The confined N-dimensional harmonic oscillator revisited,” Physica Scripta, vol. 81, Article ID 045010, 2010.
- 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.
- 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.
- Y. P. Varshni, “Critical cage radii for a confined hydrogen atom,” Journal of Physics B, vol. 31, no. 13, p. 2849, 1998.
- S. M. Al-Jaber, “A confined -dimensional harmonic oscillator,” International Journal of Theoretical Physics, vol. 47, no. 7, pp. 1853–1864, 2008.
- 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.
- 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.
- 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.
- 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.
- M. Reed and B. Simon, Methods of Modern Mathematical Physics. IV. Analysis of Operators, Academic Press, New York, NY, USA, 1978.
- 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.
- A. Sommerfeld, Partial Differential Equations in Physics, Academic Press, New York, NY, USA, 1949.
- 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.
- 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.
- 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.
- 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.
- R. L. Hall, “Complementary pictures of the -boson problem,” Physical Review A, vol. 37, pp. 2673–2679, 1988.
- 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.
- W. M. Houston, “A nuclear model,” Physical Review, vol. 47, no. 12, pp. 942–946, 1935.
- H. R. Post, “Many-particle systems: derivation of a shell model,” Proceedings of the Physical Society, vol. 66, no. 7, p. 649, 1953.
- J. B. McGuire, “Study of exactly soluble one-dimensional -body problems,” Journal of Mathematical Physics, vol. 5, pp. 622–636, 1964.
- D. C. Mattis, The Many-Body Problem: An Encyclopedia of Exactly Solved Models in One Dimension, World Scientific, Singapore, 2009.