An Efficient and Accurate Grid Method for Solving the Time-Dependent Schroedinger Equation: Application of Coulomb Wave Function DVR to Atomic Systems in Strong Laser Fields

TL;DR

This paper introduces a Coulomb wave function DVR grid method that significantly improves the efficiency and accuracy of solving the time-dependent Schrödinger equation for atomic systems in strong laser fields, reducing computational resources.

Contribution

The paper presents a novel Coulomb wave function DVR approach that outperforms finite difference methods in efficiency and accuracy for atomic ionization simulations under intense laser pulses.

Findings

CWDVR method requires 3-10 times fewer grid points than FD methods.

Accurately describes Coulomb singularity and continuum wave functions.

Ionization rates agree well with other theoretical results.

Abstract

We present an efficient and accurate grid method for solving the time-dependent Schr\"{o}dinger equation of atomic systems interacting with intense laser pulses. As usual, the angular part of the wave function is expanded in terms of spherical harmonics. Instead of the usual finite difference (FD) scheme, the radial coordinate is discretized using the discrete variable representation which is constructed from the Coulomb wave function. For an accurate description of the ionization dynamics of atomic systems, the Coulomb wave function discrete variable representation (CWDVR) method needs 3-10 times less grid points than the FD method. The resultant grid points of CWDVR distribute unevenly so that one has finer grid near the origin and coarser one at larger distances. The other important advantage of the CWDVR method is that it treats the Coulomb singularity accurately and gives a good representation of continuum wave functions. The time propagation of the wave function is implemented using the well-known Arnoldi method. As examples, the present method is applied to the multiphoton ionization of both H and H$^-$ in intense laser fields. Short-time excitation and ionization dynamics of H by static electric fields is also investigated. For a wide range of photon energies and laser intensities, ionization rates calculated using this method are in excellent agreement with those from other theoretical calculations.