Time-dependent embedding

TL;DR

This paper introduces a novel method for solving the time-dependent Schrödinger equation using an embedding approach that simplifies boundary conditions by incorporating an embedding term derived from the Fourier transform of the energy-dependent embedding potential.

Contribution

The paper presents a new time-dependent embedding technique based on Fourier transforms, enabling explicit treatment of a finite spatial region in Schrödinger equation simulations.

Findings

Successfully applied to a 1D atomic model in electric fields

Demonstrated surface excitation calculations at a jellium surface

Validated method with results consistent with known physics

Abstract

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 embedding term added on to the Hamiltonian. This time-dependent embedding term is derived from the Fourier transform of the energy-dependent embedding potential, which embeds the time-independent Schr\"odinger equation. Results are presented for a one-dimensional model of an atom in a time-varying electric field, the surface excitation of this model atom at a jellium surface in an external electric field, and the surface excitation of a bulk state.