Abstract
Suitable scaling for the time-dependent Schrödinger equation allows reduction of various types of time-dependent Schrödinger hamiltonians to the quantum dynamics of the harmonic oscillator. Therefore perturbing any of these time-dependent hamiltonians amounts to perturbing the harmonic oscillator's hamiltonian by suitable time-dependent perturbations. The particular case of time-periodic perturbations of the harmonic oscillator is then considered with regard to the “quantum stability problem”. Quantum stability results are obtained, away from some resonant set of Lebesgue measure smaller than ε (any ε), provided a suitable norm of the perturbation is dominated by Cε (some constant C).
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
