On energy gaps in a new type of analytically solvable model in quantum mechanics

DOI10.1016/0022-247X(88)90003-0zbMath0669.47002OpenAlexW2033828368MaRDI QIDQ1118792

Werner Kirsch, Friedrich Gesztesy, Helge Holden

Publication date: 1988

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-247x(88)90003-0

zbMATH Keywords

independent identically distributed random variablesSaxon- Hutner conjecturespectral properties of one-dimensional Schrödinger Hamiltonians

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Spectrum, resolvent (47A10)

Related Items

The phase formalism for one-dimensional random Schrödinger operators ⋮ New analytically solvable models of relativistic point interactions ⋮ Spectra of periodic Schrödinger operators on the degenerate zigzag nanotube with \(\delta\) type vertex conditions ⋮ Geometry of the Saxon-Hutner theorem. ⋮ Asymptotic estimates for the spectral gaps of the Schrödinger operators with periodic \(\delta'\)-interactions ⋮ Coexistence problem for the one-dimensional Schrödinger operators with the double or triple periodic \(\delta ^{(1)}\)-interactions ⋮ Spectral gaps of the Schrödinger operators with periodic δ′-interactions and Diophantine approximations ⋮ Generalized Kronig-Penney Hamiltonians ⋮ A duality between Schroedinger operators on graphs and certain Jacobi matrices ⋮ A relativistic method for the nonrelativistic gap problem ⋮ Transport in the random Kronig-Penney model ⋮ Spectral asymptotics for Schrödinger operators with periodic point interactions

Cites Work

• One-dimensional Schrödinger operators with ergodic potential
• The spectrum of defect periodic point interactions
• Almost periodic Schrödinger operators: A review
• Support theorems for random Schrödinger operators
• Infinite representability of Schrödinger operators with ergodic potential
• New analytically solvable models of relativistic point interactions
• On the spectrum of Schrödinger operators with a random potential
• The energy spectrum of an amorphous substance
• Disordered One-Dimensional Crystals
• A new class of solvable models in quantum mechanics describing point interactions on the line
• Quantum mechanics of electrons in crystal lattices
• Periodic Impurities in a Periodic Lattice
• Single Band Motion of Conduction Electrons in a Uniform Magnetic Field
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