Coulomb-Zeeman-Stark problem in two dimensions

Coulomb-bound systems in reduced dimensions are sensitive probes of increased confinement. For example, the ground-state binding energy of hydrogen atoms increases by a factor of 4 when passing from three to two dimensions. Recently, quasi-two-dimensional hydrogen has been realized experimentally in the form of low-dimensional excitons. Their sensitivity to external electric and magnetic perturbations is reduced by the confinement. To quantify the reduction, we consider in the present work two-dimensional hydrogen in crossed electric and magnetic fields. We compare analytical, numerical, and variational results for the binding energy and dipole polarizability in arbitrary magnetic fields. Our analytical expressions for both weak and strong magnetic fields are supplemented by accurate variational and hypergeometric resummation results, thereby covering arbitrary magnetic fields.