Quantum scattering with time-decaying harmonic oscillators

Abstract

By controlling coefficients and decaying order of time-decaying harmonic potentials, the velocity of a quantum particle is decelerated by the effect of harmonic potentials but the particle is non-trapping. In this paper, we consider the quantum system with controlled harmonic potentials. By defining the wave operators for this system and suitable range of these, we can prove the existence and completeness of wave operators with respect to the short-range potentials $V(t,x)$ satisfying $|V(t,x)|=o((1+|x|{)}^{-1/(1-\lambda )})$, for some $\lambda$, $0<\lambda <1/2$.

Cited by in corpus (4)

• Critical scattering in a time-dependent harmonic oscillator
• Asymptotic behavior of solutions to nonlinear Schrödinger equations with time-dependent harmonic potentials
• Strichartz estimates for Schrödinger operators with square potential with time-dependent coefficients
• Final state problem for nonlinear Schrödinger equations with time-decaying harmonic oscillators