We provide an exact version of the Egorov Theorem for a class of Schrödinger operators in 2(), where =ℝ/2ℤ 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 do in order to recover the Schrödinger operator. This result turns out to be strictly related to the Bohr-Sommerfeld quantization rules as well as to the inverse spectral problem and the periodic homogenization of Hamilton–Jacobi equations.
A. Parmeggiani, L. Zanelli (2019). An Exact Version of the Egorov Theorem for Schrödinger Operators in L2(T). JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 25(4), 1759-1781 [10.1007/s00041-018-09646-w].
An Exact Version of the Egorov Theorem for Schrödinger Operators in L2(T)
A. Parmeggiani
;
2019
Abstract
We provide an exact version of the Egorov Theorem for a class of Schrödinger operators in 2(), where =ℝ/2ℤ 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 do in order to recover the Schrödinger operator. This result turns out to be strictly related to the Bohr-Sommerfeld quantization rules as well as to the inverse spectral problem and the periodic homogenization of Hamilton–Jacobi equations.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
