Asymptotic quantum degeneracy at a 2D corner

TL;DR

This paper explores a novel form of asymptotic degeneracy in quantum mechanics occurring at a 2D surface formed by intersecting planes with an angle greater than pi, demonstrated through a charged particle in a polarizable wedge.

Contribution

It introduces a new type of asymptotic degeneracy specific to particles bound to wedge-shaped surfaces with angles exceeding pi, expanding understanding of quantum surface states.

Findings

Identification of asymptotic degeneracy at wedge intersections with angles > pi

Demonstration using a charged particle in a polarizable wedge

Analysis of bound states as a function of wedge angle

Abstract

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.