An elementary exposition of the Efimov Effect

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.