An Exact Version of the Egorov Theorem for Schrödinger Operators in L2(T)

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