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Landau-level splitting by a circular $δ$ interaction: boundary overlap and the hard-wall crossover
A thin circular barrier lifts the angular momentum degeneracy of Landau states according to their overlap with the barrier. We quantify this effect for the two-dimensional Landau Hamiltonian with a circular $δ$ interaction of radius $a$ and strength $α$. Starting from the known Kummer-function match
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