%0 Journal Article
%T Pure Point Spectrum of the Floquet Hamiltonian for the Quantum Harmonic Oscillator Under Time Quasi- Periodic Perturbations
%A W. -M. Wang
%J Mathematics
%D 2008
%I arXiv
%R 10.1007/s00220-007-0379-z
%X We prove that the $1-d$ quantum harmonic oscillator is stable under spatially localized, time quasi-periodic perturbations on a set of Diophantine frequencies of positive measure. This proves a conjecture raised by Enss-Veselic in their 1983 paper \cite{EV} in the general quasi-periodic setting. The motivation of the present paper also comes from construction of quasi-periodic solutions for the corresponding nonlinear equation.
%U http://arxiv.org/abs/0805.3764v1