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.
An Exact Version of the Egorov Theorem for Schrödinger Operators in L2(T) / A. Parmeggiani; L. Zanelli. - In: JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS. - ISSN 1069-5869. - STAMPA. - 25:4(2019), pp. 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.