Related papers: Recursive Schr\" odinger Equation Approach to Fast…
The master equation describing non-equilibrium one-dimensional problems like diffusion limited reactions or critical dynamics of classical spin systems can be written as a Schr\"odinger equation in which the wave function is the probability…
Atomic and molecular breakup reactions, such as multiple-ionisation, are described by a driven Schr\"odinger equation. This equation is equivalent to a high-dimensional Helmholtz equation and it has solutions that are outgoing waves,…
We investigate discretizations of the integrable discrete nonlinear Schr\"odinger dynamical system and related symplectic structures. We develop an effective scheme of invariant reducing the corresponding infinite system of ordinary…
In this study, a recursive solution technique in conjunction with generalized integrating factors is presented and applied to address first and second order linear differential equations. This approach demonstrates practical utility in…
We introduce a new iterative method to recover a real compact supported potential of the Schr\"odinger operator from their fixed angle scattering data. The method combines a fixed point argument with a suitable approximation of the…
This paper improves the convergence and robustness of a multigrid-based solver for the cross sections of the driven Schroedinger equation. Adding an Coupled Channel Correction Step (CCCS) after each multigrid (MG) V-cycle efficiently…
A quantum mechanical description of particle propagation on the discrete spacetime of a causal set is presented. The model involves a discrete path integral in which trajectories within the causal set are summed over to obtain a particle…
In this paper we prove dispersive estimates for the system formed by two coupled discrete Schr\"odinger equations. We obtain estimates for the resolvent of the discrete operator and prove that it satisfies the limiting absorption principle.…
We construct explicit integral relations between propagators of generalized Schr\"odinger equations that are linked by higher-order supersymmetry. Our results complement and extend the findings obtained in J. Phys.A 40, 10557 (2007) for the…
A method for obtaining discretization formulas for the derivatives of a function is presented, which relies on a generalization of divided differences. These modified divided differences essentially correspond to a change of the dependent…
This article deals with the numerical integration in time of nonlinear Schr\"odinger equations. The main application is the numerical simulation of rotating Bose-Einstein condensates. The authors perform a change of unknown so that the…
The goal of this paper is to provide an analysis of the "toolkit" method used in the numerical approximation of the time-dependent Schr\"odinger equation. The "toolkit" method is based on precomputation of elementary propagators and was…
The Schr\"odinger equation defines the dynamics of quantum particles which has been an area of unabated interest in physics. We demonstrate how simple transformations of the Schr\"odinger equation leads to a coupled linear system, whereby…
We propose a family of reliable symplectic integrators adapted to the Discrete Non-Linear Schr\"odinger equation; based on an idea of Yoshida (H. Yoshida, Construction of higher order symplectic integrators, Physics Letters A, 150, 5,6,7,…
Nonlinear and dispersive transmission impairments in coherent fiber-optic communication systems are often compensated by reverting the nonlinear Schr\"odinger equation, which describes the evolution of the signal in the link, numerically.…
By returning to the underlying discrete time formalism, we relate spurious results in coherent state path integral calculations to the high frequency structure of their propagators. We show how to modify the standard expressions for…
By constructing the commutative operators chain, we derive the integrable conditions for solving the eigenfunctions of Dirac equation and Schr\"odinger equation. These commutative relations correspond to the intrinsic symmetry of the…
We propose a new procedure by using the recursive Green's functions which remove all the repetition terms from the time-independent perturbation series for finite-level quantum systems. These Green's functions are introduced as a…
In this paper we present a perturbative procedure that allows one to numerically solve diffusive non-Markovian Stochastic Schr\"odinger equations, for a wide range of memory functions. To illustrate this procedure numerical results are…
Consider a bounded solution of the focusing, energy-critical wave equation that does not scatter to a linear solution. We prove that this solution converges in some weak sense, along a sequence of times and up to scaling and space…