Abstract
We consider the theoretical problem of finding the bound eigenstates of an infinite nonuniform two-dimensional waveguide with Dirichlet boundary conditions. Using a coordinate transformation we show that this is equivalent to finding the eigenstates of a uniform waveguide with a potential proportional to the eigenvalue. Hence there is a sense in which the bound states occurring in nonuniform waveguides are analogous to bound states due to potentials in uniform waveguides.
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