We solve the problem of a neutral atom interacting with a charged wire, giving rise to an attractive 1/r² potential in two dimensions. We show how a suitable average over all possible self-adjoint extensions of the radial Schr\"odinger Hamiltonian eventually leads to the classical formula for absorption of the atom, a formula shown to be in agreement with a recent experiment.
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Bawin et al. (2001) studied this question.
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