Modeling of Coulomb interaction in parabolic quantum wires

We study the exciton states in a parabolic quantum wire. An exactly solvable model is introduced for calculating the exciton state and the binding energy as a function of the radius of the quantum wire within the envelope-function approximation. In the calculation, we replace the actual Coulomb interaction between the electron and the hole by a Gaussian nonlocal separable potential and obtain closed expressions for both the envelope-function and the binding energy. Results are compared with those obtained by perturbative methods.