A new method is proposed for calculating the displacements due to an edge or screw dislocation in a crystal. The dislocation is represented by a perturbation in the phonon state of a perfect crystal and the treatment is carried out by the use of second quantization. The results agree with the classical ones at large distances from the dislocation core but show a quite different structure in the neighbourhood of the core which eliminates the singularities in the former theory.
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Galotto et al. (1965) studied this question.
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