Quadratic zeeman effect in hydrogen atoms in a uniform magnetic field of arbitrary strength

Abstract

The quadratic Zeeman effect in the hydrogen atom in a uniform magnetic field is studied for arbitrary field strengths. A set of discrete square-integrabel ($L^2$) functions which have the particular characteristic of containing both scale factors of Coulomb and magnetic fields is proposed as a suitable basis set for the purpose. A number of sumrules are calculated to demonstrate that the basis set can be used for the construction of an approximate $L^2$ representation of the resolvent operator for the hydrogen atom in a magnetic field. As an application, we calculate the dipole polarizabilities of the ground state and the decay rates of 2s state of the hydrogen atom for different values of magnetic field strength including the transition region from Coulombic to magnetic dominance.