On the bound states of magnetic Laplacians on wedges

This note is mainly inspired by the conjecture [33, Conj. 8.10] about the existence of bound states for magnetic Neumann Laplacians on planar wedges of any aperture φ ∈ (0, π). So far, a proof was only obtained for apertures φ . 0.511π. The conviction in the validity of this conjecture for apertures φ & 0.511π mainly relied on numerical computations. In this note we succeed to prove the existence of bound states for any aperture φ . 0.583π using a variational argument with suitably chosen test functions. Employing some more involved test functions and combining a variational argument with numerical optimisation, we extend this interval up to any aperture φ . 0.595π. Moreover, we analyse the same question for closely related problems concerning magnetic Robin Laplacians on wedges and for magnetic Schrödinger operators in the plane with δ-interactions supported on broken lines.