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Register a new userOn reducibility of Quantum Harmonic Oscillator on $mathbb{R}^d$ with quasiperiodic in time potential
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Eric Paturel
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We prove that a linear d-dimensional Schr{o}dinger equation on $mathbb{R}^d$ with harmonic potential $|x|^2$ and small t-quasiperiodic potential $ipartial_t u -- Delta u + |x|^2 u + epsilon V (tomega, x)u = 0, x in mathbb{R}^d$ reduces to an autonomous system for most values of the frequency vector $omega in mathbb{R}^n$. As a consequence any solution of such a linear PDE is almost periodic in time and remains bounded in all Sobolev norms.
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