2022/07/01 by Simen Kvaal, Caroline Lasser, Kvaal, Simen +5 · 3 citations
Engineering · Mathematics · Physics and Astronomy · #Advanced Fiber Laser Technologies #Algorithm #Applied mathematics #Chemical Physics (physics.chem-ph) #Computer science #Dimension (graph theory) #FOS: Physical sciences #Gaussian #Geometry #Grid #Laser-Matter Interactions and Applications #Mathematical analysis #Mathematical optimization #Mathematics #Nonlinear system #Physics #Quantum Physics (quant-ph) #Quantum mechanics #Residual #Schrödinger equation #Solver #Terahertz technology and applications
paper · pdf · doi:10.48550/arxiv.2207.00271
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2022/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Linear combinations of complex gaussian functions, where the linear and nonlinear parameters are allowed to vary, are shown to provide an extremely flexible and effective approach for solving the time-dependent Schrödinger equation in one spatial dimension. The use of flexible basis sets has been proven notoriously hard within the systematics of the Dirac--Frenkel variational principle. In this work we present an alternative time-propagation scheme that de-emphasizes optimal parameter evolution but directly targets residual minimization via the method of Rothe's method, also called the method of vertical time layers. We test the scheme using a simple model system mimicking an atom subjected to an extreme laser pulse. Such a pulse produces complicated ionization dynamics of the system. The scheme is shown to perform very well on this model and notably does not rely on a computational grid. Only a handful of gaussian functions are needed to achieve an accuracy on par with a high-resolution, grid-based solver. This paves the way for accurate and affordable solution of the time-dependent Schrödinger equation for atoms and molecules within and beyond the Born--Oppenheimer approximation.