Localized states in arbitrarily shaped quantum wire: A variation-perturbation technique

In this paper we present a variational technique for calculating the energy levels in a confined system with a complex shape and finite boundary conditions. The general method is applied to the case of a deformed cylindrical quantum wire and it is shown that in this case the single particle Schrodinger equation can be reduced to a set of coupled one-dimensional equations. These equations, containing an effective potential depending on the wire geometry and boundary conditions, can be solved by means of a perturbation expansion. It is shown that the calculated perturbation corrections become important only when a sharp deformation is considered.