We provide an exact version of the Egorov Theorem for a class of Schrödinger oper- ators in $L^2(Bbb T)$, where $Bbb T = Bbb R / 2 pi Bbb Z$ is the one-dimensional torus. We show that the classical Hamiltonian, after the symplectic transformation to action coordinates, can be composed with a toroidal semiclassical ψdo in order to recover the Schrödinger operator. This result turns out to be strictly related to the Bohr-Sommerfeld quantiza- tion rules as well as to the inverse spectral problem and the periodic homogenization of Hamilton-Jacobi equations.

An Exact Version of the Egorov Theorem for Schrödinger Operators in $L^2 (Bbb T)$

lorenzo zanelli;
2019

Abstract

We provide an exact version of the Egorov Theorem for a class of Schrödinger oper- ators in $L^2(Bbb T)$, where $Bbb T = Bbb R / 2 pi Bbb Z$ is the one-dimensional torus. We show that the classical Hamiltonian, after the symplectic transformation to action coordinates, can be composed with a toroidal semiclassical ψdo in order to recover the Schrödinger operator. This result turns out to be strictly related to the Bohr-Sommerfeld quantiza- tion rules as well as to the inverse spectral problem and the periodic homogenization of Hamilton-Jacobi equations.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/3285867
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