# Fourth order real space solver for the time-dependent Schrödinger equation with singular Coulomb potential

@article{Majorosi2016FourthOR, title={Fourth order real space solver for the time-dependent Schr{\"o}dinger equation with singular Coulomb potential}, author={Szil{\'a}rd Majorosi and Attila Czirj{\'a}k}, journal={Comput. Phys. Commun.}, year={2016}, volume={208}, pages={9-28} }

## Figures and Tables from this paper

## 12 Citations

Automated Selection of the Computational Parameters for the Higher-Order Parabolic Equation Numerical Methods

- Computer Science, MathematicsICCSA
- 2020

This paper considers a finite-difference split-step Padé method for the one-way Helmholtz equation and a discrete dispersion relation based algorithm for finding the optimal computational parameters of the numerical method is presented.

Coulomb-Corrected Strong Field Approximation without Singularities and Branching Points

- PhysicsJournal of Physics: Conference Series
- 2019

The domain of validity of the Coulomb-Corrected Strong-Field Approximation (CCSFA) is going to be analyzed in relation to the semi-classical dynamics of electrons during ionization of hydrogen-like…

Density-based one-dimensional model potentials for strong-field simulations in He,
H2+
, and
H2

- PhysicsPhysical Review A
- 2020

We present results on the accurate one-dimensional (1D) modeling of simple atomic and molecular systems excited by strong laser fields. We use atomic model potentials that we derive from the…

Improved one-dimensional model potentials for strong-field simulations

- PhysicsPhysical Review A
- 2018

Based on a plausible requirement for the ground-state density, we introduce an alternative one-dimensional (1D) atomic model potential for the 1D simulation of the quantum dynamics of a single active…

Quantum entanglement in strong-field ionization

- Physics
- 2017

We investigate the time-evolution of quantum entanglement between an electron, liberated by a strong few-cycle laser pulse, and its parent ion-core. Since the standard procedure is numerically…

Quantum interference in strong-field ionization by a linearly polarized laser pulse and its relevance to tunnel exit time and momentum

- PhysicsPhysical Review A
- 2021

We investigate the liberation of an atomic electron by a linearly polarized single-cycle nearinfrared laser pulse having a peak intensity that ensures tunneling. Based on phase space analysis and…

Theoretical investigation of the negative ionization of hydrogen particles on metal surfaces with low work function

- PhysicsPlasma Research Express
- 2020

This work addresses the negative ionization of hydrogen particles on low work function metal surfaces, which is an important process for the field of the surface plasma negative ion beams sources. We…

Theoretical calculation of the hydrogen negative ionization probability on the low work function surfaces

- PhysicsSEVENTH INTERNATIONAL SYMPOSIUM ON NEGATIVE IONS, BEAMS AND SOURCES (NIBS 2020)
- 2021

In this work, the probability of negative ionization of hydrogen particles on low work function metal surfaces is calculated: an important parameter for the field of the surface plasma negative ion…

Probability of the Negative Ionization of Hydrogen, Deuterium, Tritium, and Muonium on Metal Surfaces: A Theoretical Study

- Bulletin of the Russian Academy of Sciences: Physics
- 2022

## References

SHOWING 1-10 OF 87 REFERENCES

A high-order accuracy method for numerical solving of the time-dependent Schrödinger equation

- Mathematics
- 1999

Numerical solver of the time-dependent Schrödinger equation with Coulomb singularities

- Computer Science
- 2006

This paper addresses a very fundamental and important problem in the numerical analysis of atomic and molecular systems: How to discretize Hamiltonians with divergent potential terms, such as Coulomb singularities by using the known asymptotic form of the wave function near the singularity instead of the (nonexistent) Taylor series.

Fourth order gradient symplectic integrator methods for solving the time-dependent Schrödinger equation

- Computer Science
- 2000

We show that the method of splitting the operator ee(T+V) to fourth order with purely positive coefficients produces excellent algorithms for solving the time-dependent Schrodinger equation. These…

Solving the time-dependent Schrödinger equation numerically.

- MathematicsPhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1994

The scheme is a straightforward extension of the second order differencing scheme to the fourth, sixth, and higher order accuracy and is much more accurate than CN, almost equal to CH.

Parallel solver for the time-dependent linear and nonlinear Schrödinger equation.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2006

An approach in which the finite-element discrete variable representation (FEDVR) is combined with the real-space product (RSP) algorithm to generate an efficient and highly accurate method for the solution of the time-dependent linear and nonlinear Schrödinger equation is described.

Solution of time-independent Schrödinger equation by the imaginary time propagation method

- Computer ScienceJ. Comput. Phys.
- 2007

Any order imaginary time propagation method for solving the Schrödinger equation

- Computer Science, Physics
- 2009

Accurate numerical solutions of the time-dependent Schrödinger equation.

- MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2007

The improved method is shown to lead to feasible studies of coherent-state oscillations with additional short-range interactions, wave-packet scattering, and long-time studies of decaying systems.

EXPONENTIAL PROPAGATORS (INTEGRATORS) FOR THE TIME-DEPENDENT SCHRÖDINGER EQUATION

- Mathematics, Physics
- 2013

The time-dependent Schrodinger Equation (TDSE) is a parabolic partial differential equation (PDE) comparable to a diffusion equation but with imaginary time. Due to its first order time derivative,…