  In this paper we develop a semi-analytical perturbation-theory approach to
the calculation of the energy levels (binding energies) and wave functions of
excitons in phosphorene. Our method gives both the exciton wave function in
real and reciprocal spaces with the same ease. This latter aspect is important
for the calculation of the nonlinear optical properties of phosphorene. We find
that our results are in agreement with calculations based both on the
Bethe-Salpeter equation and on Monte Carlo simulations, which are
computationally much more demanding. Our approach thus introduces a simple,
viable, and accurate method to address the problem of excitons in anisotropic
two-dimensional materials.
