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Unusual bound or localized states

M. A. Cirone·G. Metikas·W. P. Schleich
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Abstract

We summarize unusual bound or localized states in quantum mechanics. Our guide through these intriguing phenomena is the classical physics of the upside-down pendulum. Taking advantage of the analogy between the corresponding Newton's equation of motion and the time-independent Schr\"{o}dinger equation, we discuss the zero-energy ground state in a three-dimensional, spatially oscillating, potential. Moreover, we focus on the effect of the attractive quantum anti-centrifugal potential that only occurs in a two-dimensional situation.

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M. A. Cirone, G. Metikas, W. P. Schleich. 2001-02-12. Unusual bound or localized states. https://doi.org/10.1515/zna-2001-0109

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