Gauge Transformations and Inverse Quantum Scattering with Medium-Range Magnetic Fields

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dc.creatorJung, Wolf
dc.date2004-12-30
dc.date2005-07-14
dc.date.accessioned2026-07-07T06:26:50Z
dc.date.available2026-07-07T06:26:50Z
dc.descriptionThe time-dependent, geometric method for high-energy limits and inverse scattering is applied to nonrelativistic quantum particles in external electromagnetic fields. Both the Schr"odinger- and the Pauli equations in R^2 and R^3 are considered. The electrostatic potential A_0 shall be short-range, and the magnetic field B shall decay faster than |x|^{-3/2} . A natural class of corresponding vector potentials A of medium range is introduced, and the decay and regularity properties of various gauges are discussed, including the transversal gauge, the Coulomb gauge, and the Griesinger vector potentials. By a suitable combination of these gauges, B need not be differentiable. The scattering operator S is not invariant under the corresponding gauge transformations, but experiences an explicit transformation. Both B and A_0 are reconstructed from an X-ray transform, which is obtained from the high-energy limit of S . Here previous results by Arians and Nicoleau are generalized to the medium-range situation. In a sequel paper, medium-range vector potentials are applied to relativistic scattering.
dc.description30+2 pages, updated with minor changes, new appendix contains a preview of the sequel paper
dc.identifierhttps://arxiv.org/abs/math-ph/0412096
dc.identifierhttp://arxiv.org/abs/math-ph/0412096
dc.identifierMPEJ vol 11, No 5, December 2005, 32 pp.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/97236
dc.subjectMathematical Physics
dc.subject81U40
dc.titleGauge Transformations and Inverse Quantum Scattering with Medium-Range Magnetic Fields
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