Magnetic scattering at low energy in two dimensions. (English) Zbl 0934.35140

The author considers the two-dimensional Schrödinger operator with compactly supported magnetic field \(b\) and compactly supported electric potential \(V\). Under the assumption that the total flux of \(b\) is not an integer, it is shown that the resonant space at zero energy has dimension at most two, and an asymptotic formula is obtained for the scattering amplitude when the energy tends to zero. As an application, the behaviour of the scattering amplitude is studied in the case where the magnetic field tends towards a Dirac measure.


35Q40 PDEs in connection with quantum mechanics
81U05 \(2\)-body potential quantum scattering theory
Full Text: DOI


[1] DOI: 10.1016/0022-1236(82)90084-2 · Zbl 0499.35019
[2] DOI: 10.1016/0003-4916(87)90182-5 · Zbl 0646.35074
[3] DOI: 10.1215/S0012-7094-79-04631-3 · Zbl 0448.35080
[4] J. Math. Kyoto Univ. 7 pp 513– (1972)
[5] Higher Transcendental Functions Vol II (1953) · Zbl 0051.30303
[6] Ann. Inst. Henri Poincaré 48 pp 175– (1988)
[7] Scattering Theory by the Enss Method, Mathematical Reports 1 (1983) · Zbl 0529.35004
[8] DOI: 10.1023/A:1007330512611 · Zbl 0907.47058
[9] DOI: 10.1063/1.532307 · Zbl 0916.47053
[10] DOI: 10.1103/PhysRev.115.485 · Zbl 0099.43102
[11] DOI: 10.1142/S0129055X95000190 · Zbl 0846.35097
[12] J. Math. Kyoto Univ. 34 pp 95– (1994) · Zbl 0817.35090
[13] DOI: 10.1016/0003-4916(83)90051-9 · Zbl 0554.47003
[14] Solvable Models in Quantum Mechanics (1988) · Zbl 0679.46057
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.