2019
DOI: 10.48550/arxiv.1901.00343
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A multiscale finite element method for the Schrödinger equation with multiscale potentials

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Cited by 2 publications
(6 citation statements)
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“…The construction of multiscale basis functions for time-dependent and multiscale potentials is mainly based on the approach in [7] for time-independent potentials.…”
Section: A Multiscale Finite Element Methods For Schrödinger Equationmentioning
confidence: 99%
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“…The construction of multiscale basis functions for time-dependent and multiscale potentials is mainly based on the approach in [7] for time-independent potentials.…”
Section: A Multiscale Finite Element Methods For Schrödinger Equationmentioning
confidence: 99%
“…Proposition 2.2 (Exponentially decaying property). Under the resolution condition of the coarse mesh, i.e., (7), there exist constants C > 0 and 0 < β < 1 independent of H, such that…”
Section: Define the Hamiltonian Operatormentioning
confidence: 99%
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“…When the potential is deterministic, i.e., v ε (x, ω) = v ε (x), many numerical methods have been proposed; see [4,16,39,27,15,9,8] for example. When the potential is random, few works have been done; see [40,25].…”
Section: Introductionmentioning
confidence: 99%