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The time-dependent Schr\"odinger equation (TDSE) in real space is fundamental to understanding the dynamics of many-electron quantum systems, with applications ranging from quantum chemistry to condensed matter physics and materials…
In this work we develop an approach for a molecular hydrogen ion (H2+) in the Born-Oppenheimer approximation while exposed to intense short-pulse radiation. Our starting point is the R-Matrix incorporating Time (RMT) formulation for atomic…
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…
A general {\it ab-initio} and non-perturbative method to solve the time-dependent Schr\"odinger equation (TDSE) for the interaction of a strong attosecond laser pulse with a general atom, i.e., beyond the models of quasi-one-electron or…
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…
Strong field ionization is difficult to treat theoretically due to the simultaneous need to treat bound state dynamics accurately and continuum dynamics efficiently. We address this problem by decomposing the time dependent Schroedinger…
Solving the time-dependent Schr\"odinger equation (TDSE) is pivotal for modeling non-adiabatic electron dynamics, a key process in ultrafast spectroscopy and laser-matter interactions. However, exact solutions to the TDSE remain…
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…
A method is proposed for extracting ionization amplitudes from the solution of the time-dependent Schr\"odinger equation (TDSE) describing a system in a time-dependent external field. The method is a hybrid of two earlier developed methods,…
Transparent boundary conditions for the time-dependent Schrodinger equation are implemented using the R-matrix method. The employed scattering formalism is suitable for describing open quantum systems and provides the framework for the…
A method of solving the time-dependent Schr\"odinger equation is presented, in which a finite region of space is treated explicitly, with the boundary conditions for matching the wave-functions on to the rest of the system replaced by an…
We show that the time-dependent Schr\"odinger equation (TDSE) is the phenomenological dynamical law of evolution unraveled in the classical limit from a timeless formulation in terms of probability amplitudes conditioned by the values of…
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 Schr\"odinger equation in one…
We derive a new time-dependent Schr\"odinger equation(TDSE) for quantum models with non-hermitian Hamiltonian. Within our theory, the TDSE is symmetric in the two Hilbert spaces spanned by the left and the right eigenstates, respectively.…
We present a wave-function based method to solve the time-dependent many-electron Schr\"odinger equation (TDSE) with special emphasis on strong-field ionization phenomena. The theory builds on the configuration-interaction (CI) approach…
We show that a pseudospectral representation of the wavefunction using multiple spatial domains of variable size yields a highly accurate, yet efficient method to solve the time-dependent Schr\"odinger equation. The overall spatial domain…
The purpose of this document is to describe the solution and implementation of the time-independent and time-dependent Schr\"odinger using pseudospectral methods. Currently, the description is for single particle systems interacting with a…
A strategy is developed for writing the time-dependent Schr\"{o}dinger Equation (TDSE), and more generally the Dyson Series, as a convolution equation using recursive Fourier transforms, thereby decoupling the second-order integral from the…
We present a novel approach for solving the time-dependent Schr\"{o}dinger equation (TDSE). The method we propose converts the TDSE to an equivalent Volterra integral equation; introducing a global Lagrange interpolation of the integrand…
Time double-slit interference experiments have been achieved and presented as complementary to spatial double-slit interference experiments, providing a further confirmation of the wave-particle duality. Numerical solutions of the free…