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arXiv · 1501.04949

Gabor Frames of Gaussian Beams for the Schrödinger equation

Michele Berra·Martina Bulai·Elena Cordero·Fabio Nicola
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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 $\hbar$-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 $\hbar$. Nonlinear parametrices, in the spirit of the nonlinear approximation, are also presented. Numerical experiments are exhibited to compare our results with the early literature.

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Michele Berra, Martina Bulai, Elena Cordero, Fabio Nicola. 2015-01-27. Gabor Frames of Gaussian Beams for the Schrödinger equation. https://arxiv.org/abs/1501.04949

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