An exact version of the Egorov theorem for Schrödinger operators in \(L^2(\mathbb {T})\)
DOI10.1007/S00041-018-09646-WzbMath1469.34116OpenAlexW2897746732MaRDI QIDQ2003611
Lorenzo Zanelli, Alberto Parmeggiani
Publication date: 9 July 2019
Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00041-018-09646-w
Schrödinger operatorsinverse spectral problemsemiclassical analysisEgorov theoremtoroidal pseudodifferential calculustoroidal semiclassical admissible operators
Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) PDEs in connection with quantum mechanics (35Q40) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Inverse problems involving ordinary differential equations (34A55) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27) Isospectrality (58J53) Hamilton-Jacobi equations (35F21)
Cites Work
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- Wigner measures supported on weak KAM tori
- On the dynamics of WKB wave functions whose phase are weak KAM solutions of H-J equation
- Calcul fonctionnel par la transformation de Mellin et opérateurs admissibles
- Quantization of pseudo-differential operators on the torus
- Coherent states and applications in mathematical physics.
- The symbol of a function of a pseudodifferential operator
- Autour de l'approximation semi-classique. (Around semiclassical approximation)
- A mathematical approach to the effective Hamiltonian in perturbed periodic problems
- The geometry of the semiclassical wave front set for Schrödinger eigenfunctions on the torus
- Singular Bohr-Sommerfeld rules.
- Bohr-Sommerfeld rules to all orders
- Some inverse problems in periodic homogenization of Hamilton-Jacobi equations
- Schrödinger spectra and the effective Hamiltonian of weak KAM theory on the flat torus
- Mather measures selected by an approximation scheme
- Pseudo-Differential Operators and Symmetries
- Quantum monodromy and Bohr-Sommerfeld rules
- An introduction to semiclassical and microlocal analysis
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