The band structure of the general periodic Schrödinger operator with point interactions

DOI10.1007/s002200050771zbMath0966.47023OpenAlexW2036846056MaRDI QIDQ1976638

Vladimir A. Geyler, Sergio A. Albeverio

Publication date: 22 August 2001

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s002200050771

zbMATH Keywords

Cantor setperiodic Schrödinger operatorspectral gapsperiod latticepoint potentialsBrillouin zoneBethe-Sommerfeld conjecturefractal componentnon-local periodic point perturbationsWigner-Seitz cell

Mathematics Subject Classification ID

Applications of operator theory in the physical sciences (47N50) General theory of partial differential operators (47F05) Positive linear operators and order-bounded operators (47B65) Convex sets in topological linear spaces; Choquet theory (46A55)

Related Items (9)

Schrödinger operators with point interactions and radial positive definite functions ⋮ Quantum mechanics of layers with a finite number of point perturbations ⋮ On creating new essential spectrum by self-adjoint extension of gapped operators ⋮ SPECTRA OF SELF-ADJOINT EXTENSIONS AND APPLICATIONS TO SOLVABLE SCHRÖDINGER OPERATORS ⋮ Spectral properties of the Schrödinger operator with \(\delta\)-distribution ⋮ Spectral theory of Schrödinger operators with infinitely many point interactions and radial positive definite functions ⋮ Dirac Cones for Point Scatterers on a Honeycomb Lattice ⋮ Vladimir A. Geyler ⋮ Quasi-one-dimensional nanosystems in a uniform magnetic field: Explicitly solvable model

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