English

Unusual bound or localized states

Quantum Physics 2015-06-26 v1

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.

Keywords

Cite

@article{arxiv.quant-ph/0102065,
  title  = {Unusual bound or localized states},
  author = {M. A. Cirone and G. Metikas and W. P. Schleich},
  journal= {arXiv preprint arXiv:quant-ph/0102065},
  year   = {2015}
}

Comments

11 pages, 4 figures