Simulation of a Hydrogen Atom in Laser Field Using the Time-Dependent Variational Principle

TL;DR

This paper employs the time-dependent variational principle with Gaussian basis functions to efficiently solve the Schrödinger equation for a hydrogen atom in a laser field, demonstrating accuracy and potential for larger systems.

Contribution

It introduces a variational approach optimizing Gaussian basis functions for time-dependent quantum simulations, extending applicability to multi-electron systems.

Findings

Accurately reproduces finite difference solutions in 1D and 3D.

Demonstrates potential for multi-electron systems with correlated basis functions.

Shows the method's effectiveness in laser-driven quantum dynamics.

Abstract

The time-dependent variational principle is used to optimize the linear and nonlinear parameters of Gaussian basis functions to solve the time-dependent Schrodinger equation in 1 and 3 dimensions for a one-body soft Coulomb potential in a laser field. The accuracy is tested comparing the solution to finite difference grid calculations using several examples. The approach is not limited to one particle systems and the example presented for two electrons demonstrates the potential to tackle larger systems using correlated basis functions.