Journal ArticleDOI
Eigenfunction expansions associated with second-order differential equations, Part II
Edwin Hewitt,E. C. Titchmarsh +1 more
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This article is published in American Mathematical Monthly.The article was published on 1959-08-01. It has received 305 citations till now. The article focuses on the topics: Method of matched asymptotic expansions & Integral equation.read more
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Growth properties of solutions of the reduced wave equation with a variable coefficient
Journal ArticleDOI
Semiclassical analysis of low lying eigenvalues, II. Tunneling*
TL;DR: In this paper, the leading asymptotics of eigenvalue splittings of - 2 + X2V in the limit as X -- o, and where V is a non-negative potential with several zeros, are discussed.
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The mathematics of photonic crystals
TL;DR: A photonic crystal, or photonic band gap (PBG) optical material, is an artificially created periodic low-loss dielectric medium in which electromagnetic waves of certain frequencies cannot propagate The range of the prohibited frequencies is called the complete band gap as mentioned in this paper.
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Spectral and scattering theory of Schrödinger operators related to the Stark effect
TL;DR: In this paper, the spectral properties and scattering theory of operators of the formH=Hε0+V,Hウス0=−Δ+E·x were analyzed.
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Dilation analyticity in constant electric field
TL;DR: In this paper, it was shown that the techniques of dilation analyticity still can be used to discuss the long-lived states (resonances) of a system described by a Hamiltonian of the formH=−Δ+ex1+V(x).