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.
Financed by the National Centre for Research and Development under grant No. SP/I/1/77065/10 by the strategic scientific research and experimental development program:
SYNAT - “Interdisciplinary System for Interactive Scientific and Scientific-Technical Information”.