The bound states of the inverted Regge-Wheeler potential are exponentially condensed near zero energy and strongly delocalized, linking black hole overtone instability to long-range potential features.
Anomalies in Quantum Mechanics: the 1/r^2 Potential
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An anomaly is said to occur when a symmetry that is valid classically becomes broken as a result of quantization. Although most manifestations of this phenomenon are in the context of quantum field theory, there are at least two cases in quantum mechanics--the two dimensional delta function interaction and the 1/r^2 potential. The former has been treated in this journal; in this article we discuss the physics of the latter together with experimental consequences.
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Bound States of the Schwarzschild Black Hole
The bound states of the inverted Regge-Wheeler potential are exponentially condensed near zero energy and strongly delocalized, linking black hole overtone instability to long-range potential features.