Analytic solution of a two-dimensional hydrogen atom. I. Nonrelativistic theory

Abstract

The two-dimensional hydrogen problem is solved analytically. In the nonrelativistic case, exact formulas for energy eigenvalues and eigenfunctions for both the discrete and continuous parts of the spectrum, dipole matrix elements, dc Stark effect, single- and two-photon transition rates, and fine and hyperfine structures are obtained. Comparison is made between the two- and the three-dimensional cases. Some interesting aspects of the solution unique to the two-dimensional case are discussed.