Some inverse spectral results for semi-classical Schrödinger operators
Some inverse spectral results for semi-classical Schrödinger operators
We show that the Birkhoff normal form of a classical Hamiltonian H(x, ξ) = ξ 2 +V (x) at a non-degenerate minimum x 0 of the potential determines the Taylor series of the potential at x 0 , provided the eigenvalues of the Hessian are linearly independent over Q and …