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The boundary integral method for magnetic billiards. (English) Zbl 0954.81018
Summary: We introduce a boundary integral method for two-dimensional quantum billiards subjected to a constant magnetic field. It allows us to calculate spectra and wavefunctions, in particular at strong fields and semiclassical values of the magnetic length. The method is presented for interior and exterior problems with general boundary conditions. We explain why the magnetic analogues of the field-free single- and double-layer equations exhibit an infinity of spurious solutions and how these can be eliminated at the expense of dealing with (hyper-) singular operators. The high efficiency of the method is demonstrated by numerical calculations in the extreme semiclassical regime.
Reviewer: Reviewer (Berlin)

81Q50 Quantum chaos
37N20 Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics)
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