An investigation was made of bound-state solutions of the two-dimensional Schrödinger equation with a dipole potential originating from the elastic effects of a single edge dislocation. Knowledge of these states could be useful for understanding a wide variety of physical systems, including superfluid behavior along dislocations in solid 4He. A review was presented of the results obtained by previous workers, together with an improved variational estimate of the ground-state energy. The eigenvalue problem was then solved numerically, and the energy spectrum was calculated. In the dimensionless units used, a ground-state energy of -0.139 was found; which was lower than any previous estimate. A successful link was also made to the behavior of the energy spectrum as derived using semi-classical considerations.

Bound States of Edge Dislocations - the Quantum Dipole Problem in Two Dimensions. K.Dasbiswas, D.Goswami, C.D.Yoo, A.T.Dorsey: Physical Review B, 2010, 81[6], 064516