Related papers: An Error Bound for the Time-Sliced Thawed Gaussian…
Time-slicing has emerged as a strategy for incorporating semiclassical propagation into real-time path integral formulation and recovering full quantum dynamics. A central step is the decomposition of a time-evolved wave function into a…
We derive an exact analytical solution to the time-dependent Schr\"odinger equation for transmission of a Gaussian wave packet through an arbitrary potential of finite range. We consider the situation where the initial Gaussian wave packet…
We numerically compare the semiclassical ``frozen Gaussian'' Herman-Kluk propagator [Chem. Phys. 91, 27 (1984)] and the ``thawed Gaussian'' propagator put forward recently by Baranger et al. [J. Phys. A 34, 7227 (2001)] by studying the…
A propagation method for the time dependent Schr\"odinger equation was studied leading to a general scheme of solving ode type equations. Standard space discretization of time-dependent pde's usually results in system of ode's of the form…
Many approximate solutions of the time-dependent Schr\"odinger equation can be formulated as exact solutions of a nonlinear Schr\"odinger equation with an effective Hamiltonian operator depending on the state of the system. We show that…
We present an analytical closed form expression, which gives a good approximate propagator for diffusion on the sphere. Our formula is the spherical counterpart of the Gaussian propagator for diffusion on the plane. While the analytical…
We build Gaussian wave packets for the linear Schr\"odinger equation and its finite difference space semi-discretization and illustrate the lack of uniform dispersive properties of the numerical solutions as established in Ignat, Zuazua,…
A detailed exposition of highly efficient and accurate method for the propagation of the time-dependent Schr\"odinger equation is presented. The method is readily generalized to solve an arbitrary set of ODE's. The propagation is based on a…
This paper develops an analytical method of truncating inequality constrained Gaussian distributed variables where the constraints are themselves described by Gaussian distributions. Existing truncation methods either assume hard…
We present and analyse a space-time discontinuous Galerkin method for wave propagation problems. The special feature of the scheme is that it is a Trefftz method, namely that trial and test functions are solution of the partial differential…
We assessed three schemes for propagating a variable-width (thawed) Gaussian wave packet moving under the influence of Morse or double-well potentials with parameters that are chemically representative. The most rigorous scheme is based on…
We consider the expansion of wave packets governed by the free Schr\"odinger equation. This seemingly simple task plays an important role in simulations of various quantum experiments and in particular in the field of matter-wave…
The dynamics of quantum systems can be approximated by the time propagation of Gaussian wave packets. Applying a time dependent variational principle, the time evolution of the parameters of the coupled Gaussian wave packets can be…
Accurate propagation of orbital uncertainty is essential for a range of applications within space domain awareness. Adaptive Gaussian mixture-based approaches offer tractable nonlinear uncertainty propagation through splitting mixands to…
We present an ab initio approach to solve the time-dependent Schr\"odinger equation to treat electron and photon impact multiple ionization of atoms or molecules. It combines the already known time scaled coordinate method with a new high…
We investigate the validity of gaussian lower bounds for solutions to an electromagnetic Schr\"odinger equation with a bounded time-dependent complex electric potential and a time-independent vector magnetic potential. We prove that, if a…
Many problems in navigation and tracking require increasingly accurate characterizations of the evolution of uncertainty in nonlinear systems. Nonlinear uncertainty propagation approaches based on Gaussian mixture density approximations…
We propose new methods designed to numerically approximate the solution to the time dependent Schr{\"o}dinger equation, based on two types of ansatz: tensors, and approximation by a linear combination of gaussian wave packets. In both…
We propose the frozen Gaussian approximation for computation of high frequency wave propagation. This method approximates the solution to the wave equation by an integral representation. It provides a highly efficient computational tool…
We propose an efficient reconstruction algorithm named the frozen Gaussian grid-point correction (FGGC) for computing the Schr\"odinger equation in the semi-classical regime using the frozen Gaussian approximation (FGA). The FGA has…