Scaled variational computation of the energy spectrum of a two-dimensional hydrogenic donor in a magnetic field of arbitrary strength

We compute the energy levels of a 2D hydrogen atom when a constant magnetic field is applied. With the help of a mixed-basis variational method and a generalization of virial theorem, which consists in scaling the wave function, we calculate the binding energies of the 1S, 2P^- and 3D^- levels. We compare the computed energy spectra with those obtained via a generalization of the mesh point technique as well as the shifted 1/N method. We show that the variational solutions present a very good behavior in the weak and strong magnetic field regimes.