Relevant approximations to the ground-state energy for the quadratic Zeeman effect.

Abstract

The ground-state energy of the quadratic Zeeman Hamiltonian ${\mathit{p}}^{2}$/2-Z/\ensuremath{\Vert}x\ensuremath{\Vert}+${\ensuremath{\lambda}}^{2}$(${\mathit{x}}_{1}^{2}$+${\mathit{x}}_{2}^{2}$)/2 has been approached using 2+\ensuremath{\epsilon} space dimensions in conjunction with the virial and Hellmann-Feynman theorems. Series expansions to first-\ensuremath{\epsilon} order have been performed, thereby setting \ensuremath{\epsilon}=1 in the end of the calculations. The ground-state energy established in this way exhibits good accuracy for strong and very strong fields, e.g., for 1\ensuremath{\le}${10}^{3}$. However, if \ensuremath{\lambda}1, one has certain intervals in which the accuracy of this method becomes poorer.