Ruijsenaars, S. N. M. The Aharonov-Bohm effect and scattering theory. (English) Zbl 0554.47003 Ann. Phys. 146, 1-34 (1983). The scattering of electrons off a cylinder inside which there is a current-carrying solenoid is considered. There are two different viewpoints on the description of the excluded magnetic fields and they lead to different hamiltonians. The corresponding S-matrices and scattering cross sections are found and it is shown that they differ considerably for \(R/\lambda \to 0\) \((R=cylinder\) radius, \(\lambda =de\) Broglie wave length of the electron), hence an experiment could serve to verify one description and falsify the other one. The idealized situation \(R=0\) is also studied. The S-matrices are explicitely obtained, it is shown that the results are invariant under a large class of gauge transformations and an anomalous long-range behaviour of the wave and scattering operator is pointed out. Reviewer: V.Georgescu Cited in 48 Documents MSC: 47A40 Scattering theory of linear operators 81U20 \(S\)-matrix theory, etc. in quantum theory Keywords:Aharonov-Bohm effect; scattering of electrons off a cylinder inside which there is a current-carrying solenoid; excluded magnetic fields; S- matrices; scattering cross sections PDF BibTeX XML Cite \textit{S. N. M. Ruijsenaars}, Ann. Phys. 146, 1--34 (1983; Zbl 0554.47003) Full Text: DOI OpenURL References: [1] Aharonov, Y.; Bohm, D., Phys. rev., 115, 485-491, (1959) [2] Ehrenberg, W.; Siday, R.E., (), 8-21 [3] Boyer, T.H., Phys. rev. D, 8, 1679-1692, (1973) [4] Möllenstedt, G.; Bayh, W., Phys. bl., 18, 299-305, (1962) [5] Boersch, H.; Hamish, H.; Grohmann, K., Z. phys., 169, 263-272, (1962) [6] Peshkin, M.; Talmi, I.; Tassie, L.J., Ann. phys. 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