Topological properties of the Born-Oppenheimer approximation and implications for the exact spectrum

DOI10.1023/A:1010912815438zbMath0981.81028OpenAlexW151877714MaRDI QIDQ5944752

Boris I. Zhilinskiĭ, Frédéric Faure

Publication date: 10 October 2001

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

Full work available at URL: https://doi.org/10.1023/a:1010912815438

zbMATH Keywords

discrete energy spectrumfixed classical stateintegral Chern classesstationary quantum vector

Mathematics Subject Classification ID

Applications of global differential geometry to the sciences (53C80) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics (81S30) Molecular physics (81V55)

Related Items (12)

A new light on the FKMM invariant and its consequences ⋮ Rearrangement of energy bands: topological aspects ⋮ Coherent states, quantum gravity, and the Born-Oppenheimer approximation. I. General considerations ⋮ Coherent states, quantum gravity, and the Born- Oppenheimer approximation. II. Compact Lie groups ⋮ Rearrangement of energy bands: Chern numbers in the presence of cubic symmetry ⋮ Manifestation of the topological index formula in quantum waves and geophysical waves ⋮ The level crossing problem in semi-classical analysis. I: The symmetric class. ⋮ Angular momentum coupling, Dirac oscillators, and quantum band rearrangements in the presence of momentum reversal symmetries ⋮ A study of energy band rearrangement in isolated molecules by means of the Dirac oscillator approximation ⋮ Topologically coupled energy bands in molecules ⋮ The level crossing problem in semi-classical analysis. II: The Hermitian case. ⋮ Geometric currents in piezoelectricity

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