Use of the Discrete Variable Representation Basis in Nuclear Physics

TL;DR

This paper demonstrates that the discrete variable representation (DVR) basis offers an efficient and nearly optimal method for numerically representing wave functions in nuclear physics, enabling smaller basis sets and straightforward analysis.

Contribution

It introduces the use of DVR basis in nuclear physics, highlighting its advantages over traditional bases in terms of efficiency, simplicity, and convergence properties.

Findings

DVR basis achieves exponential convergence for suitable problems.

DVR basis allows smaller basis sets than harmonic oscillator basis.

DVR basis simplifies analysis of convergence properties.

Abstract

The discrete variable representation (DVR) basis is nearly optimal for numerically representing wave functions in nuclear physics: Suitable problems enjoy exponential convergence, yet the Hamiltonian remains sparse. We show that one can often use smaller basis sets than with the traditional harmonic oscillator basis, and still benefit from the simple analytic properties of the DVR bases which requires no overlap integrals, simply permit using various Jacobi coordinates, and admit straightforward analyses of the ultraviolet and infrared convergence properties.