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Lamé instantons. (English) Zbl 0989.81028
Summary: We perform a precise analytic test of the instanton approximation by comparing the exact band spectrum of the periodic Lam’e 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 e/π.
MSC:
81Q20Semi-classical techniques in quantum theory, including WKB and Maslov methods
81T10Model quantum field theories