  We investigate bound state solutions of the 2D Schr\"odinger equation with a
dipole potential originating from the elastic effects of a single edge
dislocation. The knowledge of these states could be useful for understanding a
wide variety of physical systems, including superfluid behavior along
dislocations in solid $^4$He. We present a review of the results obtained by
previous workers together with an improved variational estimate of the ground
state energy. We then numerically solve the eigenvalue problem and calculate
the energy spectrum. In our dimensionless units, we find a ground state energy
of -0.139, which is lower than any previous estimate. We also make successful
contact with the behavior of the energy spectrum as derived from semiclassical
considerations.
