  Phosphorene is a bidimensional material that has properties useful for
semiconductor devices. In this work we studied the electronic and optical
properties of this material using the $GW$ approximation and the Bethe-Salpeter
equation (BSE) methods. We stress the importance of a careful convergence study
of the most relevant parameters, and we show how they affect the result of the
calculations. A comparison with previous results is given. The QP band gap
obtained was 2.06 eV and it is in good agreement with experimental results. BSE
calculations were performed on top of $G_0W_0$ to include excitonic effects.
The absorption spectrum was analysed and an optical gap of 1.22 eV was
obtained. The calculated excitonic binding energy is 0.84 eV, also in good
agreement with experimental results.
