Accurate Bound-State Spectra for Hydrogenic Donors in GaAs--(Ga, Al)As Quantum Dots

We extend the analytical transfer matrix method (ATMM) to study the bound-state spectra for hydrogenic donors in GaAs--(Ga, Al)As quantum dots. Comparison of the energy eigenvalues from ATMM with those from the wavefunction method reveals wavefunction results show large deviation from the exact ones when the radius of quantum dots r₀ become large, whereas ATMM is better accuracy.