A high-order integrator for the Schrödinger equation with time-dependent, homogeneous magnetic field
DOI10.5802/smai-jcm.69zbMath1462.81078OpenAlexW3131036851MaRDI QIDQ2023445
Oliver Rietmann, Vasile Gradinaru
Publication date: 3 May 2021
Published in: SMAI Journal of Computational Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.5802/smai-jcm.69
numerical methodmagnetic fieldLie algebraLie groupdiscrete Fourier transformsplittingconvergence ratequantum mechanicstime-dependent Schrödinger equation
Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Applications of Lie (super)algebras to physics, etc. (17B81) Numerical methods for discrete and fast Fourier transforms (65T50) Many-body theory; quantum Hall effect (81V70) Time-dependent Schrödinger equations and Dirac equations (35Q41) Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs (65M22)
Related Items
Cites Work
- Unnamed Item
- An improved semi-Lagrangian time splitting spectral method for the semi-classical Schrödinger equation with vector potentials using NUFFT
- Numerical approximation of the Schrödinger equation with the electromagnetic field by the Hagedorn wave packets
- An exact local error representation of exponential operator splitting methods for evolutionary problems and applications to linear Schrödinger equations in the semi-classical regime
- Fourth- and sixth-order commutator-free Magnus integrators for linear and nonlinear dynamical systems
- Splitting methods for the time-dependent Schrödinger equation
- Practical symplectic partitioned Runge-Kutta and Runge-Kutta-Nyström methods
- A semi-Lagrangian time splitting method for the Schrödinger equation with vector potentials
- A splitting approach for the magnetic Schrödinger equation
- Wave Equations in Higher Dimensions
- Geometric Numerical Integration
- Solving Ordinary Differential Equations I
- Computing Semiclassical Quantum Dynamics with Hagedorn Wavepackets
- Composition constants for raising the orders of unconventional schemes for ordinary differential equations
- Quantum Theory for Mathematicians
- On the Construction and Comparison of Difference Schemes
- On the exponential solution of differential equations for a linear operator
