On the bound states of magnetic Laplacians on wedges
  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.
