Unusual bound or localized states

Details Unusual bound or localized states Unusual bound or localized states

2001-02-12

arxiv.org/abs/quant-ph/0102065v1

Z. Naturforsch, 56 a, 1-13 (2001)

Physics

Quantum Physics

11 pages, 4 figures

Scientific paper

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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