Finite-difference calculation of donor energy levels in a spherical quantum dot subject to a magnetic field

• Donor states in a spherical quantum dot subject to a magnetic field are calculated.
• The effective-mass equation is numerically solved by the finite-difference method.
• Excellent agreement with the H atom is obtained by the Richardson extrapolation.
• Variational results may either underestimate or overestimate the binding energy.
• Transition energies in a realistic dot are given in terms of the field strength.

The ground and excited states of a donor impurity at the center of a spherical quantum dot subject to a magnetic field are calculated within the effective-mass approximation. The barriers are infinitely high and the differential equation is solved by combining the finite-difference method with the Richardson extrapolation. The binding and transition energies are more accurate than the available variational values, and excellent agreement is found with the hydrogen atom. The transition energies for a medium-size quantum dot are given.