Lam'e Instantons

Abstract

We perform a precise analytic test of the instanton approximation by comparing the exact band spectrum of the periodic Lamé potential to the tight-binding, instanton and WKB approximations. The instanton result gives the correct leading behavior in the semiclassical limit, while the tight-binding approximation does even better. WKB is off by an overall factor of $\sqrt{e/\pi }$.

Comments: 4 pp, RevTeX, 4 figs, uses epsfig.sty; references added