Abstract
We present an accurate calculation of the energies of the bound states of the quantumdipole problemin two dimensions using a Rayleigh-Ritz approach. We obtain an upper bound for the energy of the ground state, which is by far the most precise in the literature for this problem. We also obtain an alternative estimate of the fundamental energy of the model performing an extrapolation of the results corresponding to different subspaces. Finally, our calculation of the energies of the first 500 states shows a perfect agreement with the expected asymptotic behavior.
Similar content being viewed by others
References
K. Dasbiswas, D. Goswami, C. D. Yoo, A.T. Dorsey, Phys. Rev. B 81, 064516 (2010)
R. Landauer, Phys. Rev. 94, 1386 (1954)
P. R. Emtage, Phys. Rev. 163, 865 (1967)
V. A. Slyusarev, K. A. Chishko, Fiz. Met. Metalloved+. 58, 877 (1984)
V. M. Nabutovskii, B. Y. Shapiro, JETP Lett+. 26, 473 (1977)
I. M. Dubrovskii, Low Temp. Phys+. 23, 976 (1997)
J. L. Farvacque, P. Fracois, Phys. Status Solidi B 223, 635 (2001)
X. L. Yang, S. H. Guo, F. T. Chan, K. W. Wong, W. Y. Ching, Phys. Rev. A 43, 1186 (1991)
E. Fattal, R. Baer, R. Kosloff, Phys. Rev. E 53, 1217 (1996)
J. P. Boyd, Chebyshev and Fourier spectral methods, 2nd edition (Dover, New York, 2001)
P. M. Stevenson, Phys. Rev. D 23, 2916 (1981)
C. M. Bender, S. A. Orszag, Advanced mathematical methods for scientists and engineers: asymptotic methods and perturbation theory (McGraw-Hill, New York, 1978)
Wolfram Research, Inc., MATHEMATICA Version 8.0′ (Wolfram Research Inc., Champaign, Illinois, 2010)
Author information
Authors and Affiliations
Corresponding author
About this article
Cite this article
Amore, P. Accurate calculation of the bound states of the quantum dipole problem in two dimensions. centr.eur.j.phys. 10, 96–101 (2012). https://doi.org/10.2478/s11534-011-0087-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.2478/s11534-011-0087-3