An elementary exposition of the Efimov Effect

Details An elementary exposition of the Efimov Effect An elementary exposition of the Efimov Effect

2010-09-14

arxiv.org/abs/1009.2713v2

Physics

Quantum Physics

4 figures. Version to appear in American Journal of Physics. Minor typos fixed

Scientific paper

Two particles that are just shy of binding may develop an infinite number of shallow bound states when a third particle is added. This counter intuitive quantum mechanical result was first predicted by V. Efimov for identical bosons interacting with a short-range pair-wise potential. The so-called Efimov effect persists even for non-identical particles, provided at least two of the three bonds are almost bound. The Efimov effect has recently been verified experimentally using ultra-cold atoms. In this article, we explain the origin of this effect using only elementary quantum mechanics, and summarize the experimental evidence for the Efimov effect. A new, simple derivation for the number of Efimov states is given in the Appendix.

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