Nonperturbative dynamical-group approach to the quadratic Zeeman effect

In this paper we consider the quadratic Zeeman effect from the point of view of scaling variational method based on the SO(4,2) dynamical group of the point Coulomb problem. In this formulation, the tilting angle is treated as a variational parameter. We scale a linear combination of the SO(4,2) basis states, solving numerically for the eigenvalues by diagonalization of the resulting matrix representation of the effective Hamiltonian. The SO(4,2) formulation has the advantage that the basis states form a complete set without the inclusion of continuum states, and furthermore, all matrix elements are calculated algebraically. The method is shown to be valid for field strengths at least as high as ${10}^{10}$ G and possibly up to ${10}^{12}$ G.