ON FORMAL QUASI-PERIODIC SOLUTIONS OF THE SCHRÖDINGER EQUATION FOR A TWO-LEVEL SYSTEM WITH A HAMILTONIAN DEPENDING QUASI–PERIODICALLY ON TIME

1999/03/24 by J. C. A. Barata, JOÃO C. A. BARATA · 2 citations
Mathematics · Physics and Astronomy · #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #chao-dyn #math-ph #math.DS #math.MP #nlin.CD #physics.optics

paper · pdf · doi:10.1142/s0129055x00000034

arxiv created 1999/03/24 · openalex publication_date 2000/01/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We consider the Schrödinger equation for a class of two-level atoms in a quasi-periodic external field for large coupling, i.e. for which the energy difference 2∊ between the unperturbed levels is sufficiently small. We show that this equation has a solution in terms of a formal power series in ∊, with coefficients which are quasi-periodical functions of the time, in analogy to the Lindstedt–Poincaré series in classical mechanics.

Citations

• Zur theorie der fast periodischen funktionen: I. Eine verallgemeinerung der theorie der fourierreihen

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