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We consider a non-relativistic two-dimensional (2D) hydrogen-like atom in aweak, static, uniform magnetic field perpendicular to the atomic plane. Withinthe framework of the Rayleigh-Schr\"odinger perturbation theory, using theSturmian expansion of the generalized radial Coulomb Green function, we deriveexplicit analytical expressions for corrections to an arbitrary planarhydrogenic bound-state energy level, up to the fourth order in the strength ofthe perturbing magnetic field. In the case of the ground state, we correct anexpression for the fourth-order correction to energy available in theliterature.

Two-dimensional hydrogen-like atom in a weak magnetic field