The present paper is devoted to the semiclassical analysis of linear Schrödinger 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 Schrödinger equations by means of ħ -Gabor frames, as recently defined by M. de Gosson, and we provide precise L2L2-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. The research that led to the present paper was partially supported by  a grant of the group GNAMPA of INdAM.

Gabor frames of Gaussian beams for the Schrödinger equation

Berra, Michele;BULAI, IULIA MARTINA;CORDERO, Elena;
2017

Abstract

The present paper is devoted to the semiclassical analysis of linear Schrödinger 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 Schrödinger equations by means of ħ -Gabor frames, as recently defined by M. de Gosson, and we provide precise L2L2-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. The research that led to the present paper was partially supported by  a grant of the group GNAMPA of INdAM.
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http://arxiv.org/abs/1501.04949
http://www.sciencedirect.com/science/article/pii/S1063520315001529
Gabor frames, Gaussian beams, Metaplectic operators, Schrödinger equation, Applied Mathematics
Berra, Michele; Bulai, Iulia Martina; Cordero, Elena; Nicola, Fabio
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/1548617
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