Nonvariational approach to impurity states in quantum wires

Abstract

While the binding energy and the ground-state wave function of a hydrogenic impurity in a strictly one-dimensional or three-dimensional system can be exactly calculated, the case of finite but small (a\ensuremath{\le}${\mathit{a}}_{\mathit{B}}$) or large (a>${\mathit{a}}_{\mathit{B}}$) wire radius a is not amenable to an exact treatment, and is usually left to the variational method as the only resort. However, the amount of computation involved in variational calculations is large and its accuracy is sometimes difficult to assess. We have developed reliable and physically motivated perturbative approaches specifically to treat the a\ensuremath{\le}${\mathit{a}}_{\mathit{B}}$ and a>${\mathit{a}}_{\mathit{B}}$ situations. The close agreement of our results with those from variational methods lends support for our simpler method as an alternative to the variational approach.