A new method was proposed which was based upon a combination of a direct variational method, and perturbation theory. It was used to calculate approximately the eigenvalues and eigenfunctions of the ground state, and of states close to it. The new method was applicable to the Schrödinger equation, with a potential that was proportional to the dilatation that was produced by an edge dislocation. The ground-state energy which was obtained in this case was lower than published theoretical values. An energy value was obtained for the state for which the eigenfunction was odd in the azimuthal angle. It was assumed that, near to the condensation point, the spectrum could be described only statistically.

A New Variational Method in the Problem of the Spectrum of Elementary Excitations in an Edge-Dislocation Crystal. I.M.Dubrovskii: Low Temperature Physics, 1997, 23[12], 976-9