Gauge-Invariant Frozen Gaussian Approximation Method for the Schrödinger Equation with Periodic Potentials

DOI10.1137/15M1040384zbMath1346.81043arXiv1509.05552MaRDI QIDQ2818242

Xu Yang, Ricardo Delgadillo, Jian-feng Lu

Publication date: 7 September 2016

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1509.05552

zbMATH Keywords

semiclassical regimeSchrödinger equationperiodic potentialfrozen Gaussian approximationgauge-invariant

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Statistical mechanics of solids (82D20) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Approximation by polynomials (41A10) Yang-Mills and other gauge theories in mechanics of particles and systems (70S15) Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory (81Q70)

Related Items

Frozen Gaussian approximation-based artificial boundary conditions for one-dimensional nonlinear Schrödinger equation in the semiclassical regime ⋮ Optimal error estimate of the extended-WKB approximation to the high frequency wave-type equation in the semi-classical regime ⋮ A Multiscale Reduced Basis Method for the Schrödinger Equation With Multiscale and Random Potentials ⋮ Efficient multiscale methods for the semiclassical Schrödinger equation with time-dependent potentials ⋮ A Hybrid Method for Computing the Schrödinger Equations with Periodic Potential with Band-Crossings in the Momentum Space ⋮ A Multiscale Finite Element Method for the Schrödinger Equation with Multiscale Potentials ⋮ Convergence analysis of the localized orthogonal decomposition method for the semiclassical Schrödinger equations with multiscale potentials

Uses Software

• GIFGA

Cites Work

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