A perturbation-variational treatment of hydrogenic impurity states in quantum wires

The binding energy of a hydrogenic impurity placed on the axis of a cylindrical quantum-well wire is studied using a perturbation-variational expansion method to the first order in the perturbation expansion. The variations of the binding energy with the radius and barrier height of the quantum-well wire are obtained. When the radius of the wire becomes very large or the barrier height of the quantum-well is very small, the impurity behaves like a free hydrogenic atom with a ground-state energy of one effective Rydberg.