The boundary integral method for magnetic billiards

We introduce a boundary integral method for two-dimensional quantum billiar ds subjected to a constant magnetic field, it allows us to calculate spectr a and wavefunctions, in particular at strong fields and semiclassical value s of the magnetic length. The method is presented for interior and exterior problems with general boundary conditions. We explain why the magnetic ana logues of the field-free single- and double-layer equations exhibit an infi nity of spurious solutions and how these can be eliminated at the expense o f dealing with (hyper-)singular operators. The high efficiency of the metho d is demonstrated by numerical calculations in the extreme semiclassical re gime.