On the stationary Schrödinger equation with a quasi-periodic potential

DOI10.1016/0378-4371(84)90269-3zbMath0601.34016OpenAlexW1976363935MaRDI QIDQ1081010

Jürgen Pöschel, Jürgen K. Moser

Publication date: 1984

Published in: Physica A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0378-4371(84)90269-3

zbMATH Keywords

spectral gapsquasi-periodic potentialstationary Schrödinger equationsecond order differential equationFloquet type solutions

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Ordinary differential operators (34L99)

Cites Work

• Smoothness of spectral subbundles and reducibility of quasi periodic linear differential systems
• An example of a Schrödinger equation with almost periodic potential and nowhere dense spectrum
• Almost periodic Schrödinger operators. I: Limit periodic potentials
• The rotation number for almost periodic potentials
• Almost periodic differential equations
• The one-dimensional Schrödinger equation with a quasiperiodic potential
• A spectral theory for linear differential systems
• Convergent series expansions for quasi-periodic motions
• PROOF OF A THEOREM OF A. N. KOLMOGOROV ON THE INVARIANCE OF QUASI-PERIODIC MOTIONS UNDER SMALL PERTURBATIONS OF THE HAMILTONIAN
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