Time decay and spectral kernel asymptotics

1089-7658

AIP Digital Archive

Mathematics

Physics

For quantum systems in R3 defined by a Hamiltonian H given as the sum of the negative Laplacian perturbed by a real-valued potential v(x), the large time behavior of the fundamental solution of the time-dependent Schrödinger equation is investigated. For a suitably restricted class of potentials that have algebraic decay as ||x||→∞, the continuous spectrum portion of the fundamental solution is characterized by an asymptotic expansion as t→±∞, which is uniform in compact subsets of R3×R3. These results are then applied to derive the large energy asymptotic expansions of the spectral kernel associated with H.

Electronic Resource