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Asymptotic quantum degeneracy at a 2D corner

In quantum mechanics, asymptotic degeneracy is often considered in the context of a particle in a symmetric double-well potential, and is the phenomenon whereby pairs of energy levels come together to form doubly degenerate levels in response to an increase in the separation, or depth of the two wells. Here we highlight a new kind of asymptotic degeneracy that can arise when a particle is bound to a surface formed by the intersection of two planes, when the intersection angle is greater than pi. To demonstrate this effect we consider the bound states of a charged particle subject its own 'image' potential in a highly polarizable wedge, as a function of the wedge opening angle.