Abstract

We have studied two different cylindrical waveguides with variable cross sections as models for quantum wires. By expanding the total wavefuction in terms of the Bessel function we have obtained an infinite set of coupled equations for the partial wave amplitude. In our models, bound states are present only in the lowest partial wave. For a simple bulge we have obtained the lowest eigenvalues, and for periodic waveguide we have found the width of the energy band.

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