Gabor frames of Gaussian beams for the Schrödinger equation
| Autor: | Iulia Martina Bulai, Elena Cordero, Michele Berra, Fabio Nicola |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Quadratic growth
Gabor frames Gaussian beams Metaplectic operators Schrödinger equation Gaussian Applied Mathematics 010102 general mathematics Mathematical analysis Order (ring theory) Semiclassical physics Gabor frames Gaussian beams Metaplectic operators Schrödinger equation Applied Mathematics Planck constant 01 natural sciences 010101 applied mathematics symbols.namesake Nonlinear system Perspective (geometry) symbols 0101 mathematics Mathematics |
| Popis: | The present paper is devoted to the semiclassical analysis of linear Schrodinger equations from a Gabor frame perspective. We consider (time-dependent) smooth Hamiltonians with at most quadratic growth. Then we construct higher order parametrices for the corresponding Schrodinger equations by means of ħ-Gabor frames, as recently defined by M. de Gosson, and we provide precise L 2 -estimates of their accuracy, in terms of the Planck constant ħ. Nonlinear parametrices, in the spirit of the nonlinear approximation, are also presented. Numerical experiments are exhibited to compare our results with the early literature. |
| Databáze: | OpenAIRE |
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