Lagrange-mesh calculations and Fourier transform

TL;DR

This paper discusses the Lagrange-mesh method's accuracy in quantum eigenvalue problems and introduces a Fourier transform approach to efficiently compute eigenfunctions and observables in momentum space.

Contribution

It demonstrates how to use Fourier transforms with Lagrange-mesh basis functions to obtain eigenfunctions and observables in momentum space.

Findings

Eigenfunctions can be efficiently computed in momentum space.

The method simplifies the calculation of observables in momentum space.

Lagrange-mesh provides high accuracy for two-body quantum problems.

Abstract

The Lagrange-mesh method is a very accurate procedure to compute eigenvalues and eigenfunctions of a two-body quantum equation. The method requires only the evaluation of the potential at some mesh points in the configuration space. It is shown that the eigenfunctions can be easily computed in the momentum space by a Fourier transform using the properties of the basis functions. Observables in this space can also be easily obtained.