%0 Journal Article
%T Unusual bound or localized states
%A M. A. Cirone
%A G. Metikas
%A W. P. Schleich
%J Physics
%D 2001
%I arXiv
%R 10.1515/zna-2001-0109
%X 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.
%U http://arxiv.org/abs/quant-ph/0102065v1