Two-dimensional negative donors in magnetic fields

A finite-difference solution of the Schrödinger equation for negative donor centers $D^{-}$ in two dimensions is presented. Our approach is of exact nature and allows us to resolve a discrepancy in the literature on the ground state of a negative donor. Detailed calculations of the energies for a number of states show that for field strengths less than $\gamma =0.117a.u.\mathrm{}$ the donor possesses one bound state, for $0.117<\mathrm{}\gamma <1.68\mathrm{}\hspace{0.5em}\mathrm{a}.\mathrm{u}.\mathrm{}$ there exist two bound states and for field strengths $\gamma >~1.68\hspace{0.5em}\mathrm{a}.\mathrm{u}.\mathrm{}$ the system possesses three bound states. Further relevant characteristics of negative donors in magnetic fields are provided.