#### Vol. 11, No. 3, 2018

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Reducibility of the quantum harmonic oscillator in $d$-dimensions with polynomial time-dependent perturbation

### Dario Bambusi, Benoît Grébert, Alberto Maspero and Didier Robert

Vol. 11 (2018), No. 3, 775–799
##### Abstract

We prove a reducibility result for a quantum harmonic oscillator in arbitrary dimension with arbitrary frequencies perturbed by a linear operator which is a polynomial of degree 2 in $\left({x}_{j},-i{\partial }_{j}\right)$ with coefficients which depend quasiperiodically on time.

##### Keywords
reducibility, harmonic oscillators, growth of Sobolev norms
##### Mathematical Subject Classification 2010
Primary: 35J10, 37K55