scientific article

zbMath0732.44004MaRDI QIDQ3357671

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Publication date: 1990

Full work available at URL: http://www.numdam.org/item?id=MSMF_1990_2_43__1_0

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zbMATH Keywords

spectral gapsHarper operatorHofstadter butterfly

Mathematics Subject Classification ID

Spectral theory and eigenvalue problems for partial differential equations (35P99) PDEs in connection with quantum mechanics (35Q40) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Classical operational calculus (44A45) Pseudodifferential operators and other generalizations of partial differential operators (35S99)

Related Items (7)

On the total bandwidth for the rational Harper's equation ⋮ Uniform asymptotic solution in the form of an Airy function for semiclassical bound states in one-dimensional and radially symmetric problems ⋮ On the Lipschitz continuity of spectral bands of Harper-like and magnetic Schrödinger operators ⋮ On the existence of embedded eigenvalues ⋮ Probabilistic averages of Jacobi operators ⋮ Fractal spectrum of periodic quantum systems in a magnetic field ⋮ On the Regularity of the Hausdorff Distance Between Spectra of Perturbed Magnetic Hamiltonians

Cites Work

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• The rotation number for almost periodic potentials
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• Stability of gaps for periodic potentials under variation of a magnetic field
• An exact effective Hamiltonian for a perturbed Landau level
• THE SPECTRAL THEORY AND THE INDEX OF ELLIPTIC OPERATORS WITH ALMOST PERIODIC COEFFICIENTS
• Semi-classical analysis for Harper's equation. III : Cantor structure of the spectrum
• ON THE SPECTRUM OF THE ONE-DIMENSIONAL SCHRÖDINGER EQUATION WITH A RANDOM POTENTIAL

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