On reducibility of Schrödinger equations with quasiperiodic in time potentials. (English) Zbl 1176.35141
Summary: We prove that a linear \(d\)-dimensional Schrödinger equation with an \(x\)-periodic and \(t\)-quasiperiodic potential reduces to an autonomous equation for most values of the frequency vector. The reduction is made by means of a non-autonomous linear transformation of the space of \(x\)-periodic functions. This transformation is a quasiperiodic function of \(t\).
MSC:
| 35Q41 | Time-dependent Schrödinger equations and Dirac equations |
| 35B15 | Almost and pseudo-almost periodic solutions to PDEs |
| 37K55 | Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems |
| 81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
| 35A22 | Transform methods (e.g., integral transforms) applied to PDEs |
References:
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