  We show that a two dimensional wormhole geometry is equivalent to a catenoid,
a minimal surface. We then obtain the curvature induced geometric potential and
show that the ground state with zero energy corresponds to a reflectionless
potential. By introducing an appropriate coordinate system we also obtain bound
states for different angular momentum channels. Our findings can be realized in
suitably bent bilayer graphene sheets with a neck or in a honeycomb lattice
with an array of dislocations or in nanoscale waveguides in the shape of a
catenoid.
