Virginia TechFassari, S.2014-04-092014-04-091989-06Fassari, S., "Spectral properties of the Kronig-Penney Hamiltonian with a localized impurity," J. Math. Phys. 30, 1385 (1989); http://dx.doi.org/10.1063/1.5283200022-2488http://hdl.handle.net/10919/47085It is shown that there exist bound states of the operator H ±λ=−(d 2/d x 2) +∑ m∈Z δ(⋅−(2m+1)π)±λW, W being an L 1(−∞,+∞) non‐negative function, in every sufficiently far gap of the spectrum of H 0=−d 2/d x 2 +∑ m∈Z δ(⋅−(2m+1)π). Such an operator represents the Schrödinger Hamiltonian of a Kronig–Penney‐type crystal with a localized impurity. The analyticity of the greatest (resp. lowest) eigenvalue of H λ (resp. H −λ) occurring in a spectral gap as a function of the coupling constant λ when W is assumed to have an exponential decay is also proven.en-USIn Copyrightbound stateseigenvaluesspectral propertiesArticle - Refereedhttp://scitation.aip.org/content/aip/journal/jmp/30/6/10.1063/1.528320https://doi.org/10.1063/1.528320