1D periodic potentials with gaps vanishing at k=0

zbMath1180.30035arXivcond-mat/0603172MaRDI QIDQ3397457

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Publication date: 22 September 2009

Full work available at URL: https://arxiv.org/abs/cond-mat/0603172

zbMATH Keywords

dispersion relationscoexistenceHill's equationdiscriminant and characteristic values of an O.D.E.energy bands and gapsintervals of stability and instabilitySchrödinger equation with periodic potentialvanishing gaps

Mathematics Subject Classification ID

Sturm-Liouville theory (34B24) Applications of operator theory in the physical sciences (47N50) General spectral theory of ordinary differential operators (34L05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Statistical mechanics of solids (82D20) Applications of operator theory to differential and integral equations (47N20) Entire functions of one complex variable (general theory) (30D20) Applications of functional analysis in quantum physics (46N50) Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) (34B30) Molecular physics (81V55) Asymptotic expansions of solutions to ordinary differential equations (34E05) Representations of entire functions of one complex variable by series and integrals (30D10) Special classes of entire functions of one complex variable and growth estimates (30D15) Applications of functional analysis to differential and integral equations (46N20) Ordinary differential operators (34L99)

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