Frozen Gaussian approximation for the fractional Schrödinger equation
arxiv(2024)
摘要
We develop the frozen Gaussian approximation (FGA) for the fractional
Schrödinger equation in the semi-classical regime, where the solution is
highly oscillatory when the scaled Planck constant ε is small. This
method approximates the solution to the Schrödinger equation by an integral
representation based on asymptotic analysis and provides a highly efficient
computational method for high-frequency wave function evolution. In particular,
we revise the standard FGA formula to address the singularities arising in the
higher-order derivatives of coefficients of the associated Hamiltonian flow
that are second-order continuously differentiable or smooth in conventional FGA
analysis. We then establish its convergence to the true solution. Additionally,
we provide some numerical examples to verify the accuracy and convergence
behavior of the frozen Gaussian approximation method.
更多查看译文
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要