Scattering of particles by long-range magnetic fields. (English) Zbl 0646.35074

The scattering of nonrelativistic particles (either quantum mechanical or classical) by a magnetic field B is studied in any dimension \(\nu\geq 2\). \(B(x)\) is allowed to decay like \(| x|^{-3/2-\delta}\) \((\delta >0)\), as \(| x| \to \infty\). Assumptions are made about the field strengths and not about the potentials. A gauge is constructed for which the unmodified wave operators exist and are complete even though the corresponding classical motion need not be asymptotically free. The result also holds for Yang-Mills fields.


35Q99 Partial differential equations of mathematical physics and other areas of application
81U99 Quantum scattering theory
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[1] Agmon, S., Ann. scuola norm. sup. Pisa II, 2, 151, (1975)
[2] Avron, J.; Herbst, I.; Simon, B., Duke math. J., 45, 847, (1978)
[3] Berthier, A.M.; Collet, P., Ann. inst. H. Poincaré A, 26, 279, (1977)
[4] Cotta-Ramusino, P.; Krüger, W.; Schrader, R., Ann. inst. H. Poincaré A, 31, 43, (1979)
[5] Enss, V., (), 1-69
[6] Enss, V., J. funct. anal., 52, 219, (1983)
[7] Enss, V., Commun. math. phys., 89, 245, (1983)
[8] Enss, V., (), 39-176, Berlin
[9] Herbst, I.W., Commun. math. phys., 35, 193, (1974)
[10] Hunziker, W., ()
[11] Knick, M., Streutheorie für schrödingeroperatoren mit langreichweitigen potentialen unter benutzung geometrischer methoden, Diplomarbeit, (1985), Bochum
[12] Kuroda, S.; Kuroda, S., J. math. soc. Japan, J. math. soc. Japan, 25, 222, (1973)
[13] Perry, P.A., Scattering theory by the enss method, (), Part 1 · Zbl 0529.35004
[14] Reed, M.; Simon, B., ()
[15] Schneider, M., Asymptotische Lösung der schrödingergleichung für langreichweitige potentiale, Diplomarbeit, (1984), Bochum
[16] Uhlenbeck, K.K., Commun. math. phys., 83, 11, (1982)
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