Title: On the bound states of magnetic Laplacians on wedges,
Abstract: This paper is mainly inspired by the conjecture about the existence of bound
states for magnetic Neumann Laplacians on planar wedges of any aperture
$\phi\in (0,\pi)$. So far, a proof was only obtained for apertures
$\phi\lesssim 0.511\pi$. The conviction in the validity of this conjecture for
apertures $\phi\gtrsim 0.511\pi$ mainly relied on numerical computations. In
this paper we succeed to prove the existence of bound states for any aperture
$\phi \lesssim 0.583\pi$ using a variational argument with suitably chosen test
functions. Employing some more involved test functions and combining a
variational argument with computer-assistance, we extend this interval up to
any aperture $\phi \lesssim 0.595\pi$. 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 $\delta$-interactions
supported on broken lines.