Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5774714 | Journal of Mathematical Analysis and Applications | 2017 | 15 Pages |
Abstract
We prove that the decay of the eigenfunctions of harmonic oscillators, uniform electric or magnetic fields is not stable under 0-order complex perturbations, even if bounded, of these Hamiltonians, in the sense that we can produce solutions to the evolutionary Schrödinger flows associated to the Hamiltonians, with a stronger Gaussian decay at two distinct times. We then characterize, in a quantitative way, the sharpest possible Gaussian decay of solutions as a function of the oscillation frequency or the strength of the field, depending on the Hamiltonian which is considered. This is connected to the Hardy's Uncertainty Principle for free Schrödinger evolutions.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
B. Cassano, L. Fanelli,