The relation between the off-shell Coulomb wavefunction in the momentum representation and the off-shell Coulomb T matrix, derived from standard formulae in quantum scattering theory, is investigated. The on-shell singularities of these quantities are examined and it is shown how they may be regularised in a consistent way by modifying the standard formulae, to take account of the long-range nature of the Coulomb potential in terms of distorted plane and spherical waves in the momentum representation.
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M J Roberts (1985) studied this question.
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