Hydrogenic impurity in a quantum dot: Comparison between the variational and strong perturbation methods

A comparison is given between the variational and strong perturbation techniques. It has been shown that the variational method gives, in general, better results. Also, a new formulation is presented for the strong perturbation technique that depends on a simpler equivalent form of the perturbed part of the Hamiltonian. Moreover, common expressions which are valid for both treatments have been obtained. The results are applied to calculate the binding energy for a hydrogenic impurity placed in a finite confining potential spherical quantum dot in the states (1s), (2p) and (2s). The results obtained hitherto for a central impurity by using the strong perturbation technique are deduced in a much simpler way. As regards the off-central impurity some new expressions have been derived in both treatments. The numerical results for the two states (1s) and (2p) have also been investigated.