We consider states localized by electrostatic potentials in phosphorene using an atomistic tight binding approach. From the results of the tight-binding calculations of the confined states we extract effective masses for the conduction band electrons in the armchair and zigzag directions. The masses derived in this way are used for a simple single-band effective mass model which, as we find, reproduces very well the tight-binding energy spectrum in external magnetic field, the probability densities and the interaction effects. Both methods produce Wigner crystallization for the ground-state of the electron pair with the single-electron islands separated in the armchair direction already for small quantum dots.
