Spectral properties of the Kronig--Penney Hamiltonian with a localized impurity

Journal Article · Thu Jun 01 04:00:00 EDT 1989 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.528320· OSTI ID:6318119

Fassari, S

It is shown that there exist bound states of the operator H/sub +- //sub lambda/ = -(d/sup 2//dx/sup 2/) +summation/sub m//sub element of//sub Z/delta(x-(2m+1)..pi..) +- lambdaW, W being an L/sup 1/(-infinity,+infinity) non-negative function, in every sufficiently far gap of the spectrum of H/sub 0/ = -d/sup 2//dx/sup 2/ +summation/sub m//sub element of//sub Z/delta(x-(2m+1)..pi..). Such an operator represents the Schroedinger Hamiltonian of a Kronig--Penney-type crystal with a localized impurity. The analyticity of the greatest (resp. lowest) eigenvalue of H/sub lambda/ (resp. H/sub -//sub lambda/) occurring in a spectral gap as a function of the coupling constant lambda when W is assumed to have an exponential decay is also proven.

• Research Organization: Department of Mathematics, and Center for Transport Theory and Mathematical Physics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061
• OSTI ID: 6318119
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 30:6; ISSN JMAPA
• Country of Publication: United States
• Language: English

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