Automatic grid construction for few-body quantum mechanical calculations

TL;DR

This paper presents an algorithm for creating optimized nonuniform grids to improve the accuracy of few-body quantum calculations, demonstrated on helium trimer bound states.

Contribution

The paper introduces a novel grid construction algorithm tailored for few-body quantum systems, enhancing numerical accuracy with fewer grid points.

Findings

Optimized grids accurately reproduce low-energy spectra.

Application to He trimers shows improved calculation efficiency.

Grid method reduces computational resources needed.

Abstract

An algorithm for generating optimal nonuniform grids for solving the two-body Schr\"odinger equation is developed and implemented. The shape of the grid is optimized to accurately reproduce the low-energy part of the spectrum of the Schr\"odinger operator. Grids constructed this way are applicable to more complex few-body systems where the number of grid points is a critical limitation to numerical accuracy. The utility of the grid generation for improving few-body calculations is illustrated through an application to bound states of He trimers.