Discrete Variable Representation method in the study of few-body quantum systems with non-zero angular momentum

TL;DR

This paper develops and applies a discrete-variable representation (DVR) method to accurately compute binding energies and wave functions of few-body quantum systems with non-zero angular momentum, especially those with weak, localized interactions.

Contribution

The paper introduces a DVR approach tailored for few-body quantum systems with non-zero angular momentum, improving computational efficiency and accuracy.

Findings

Binding energies of helium and lithium systems were successfully calculated.

The DVR method significantly reduces computation time for Hamiltonian matrix elements.

The approach effectively handles weak, localized potentials in quantum systems.

Abstract

The systems with small binding energies and widely distributed in space bound-state wave functions are considered. Because the interaction potential is weak and rather localized compared to the characteristic sizes of wave functions of these systems, the problem of an accurate determination of binding energy and wave functions is complicated. An essential part of the study is the development and application of the discrete-variable representation (DVR) method. This method is based on the determination of basis functions and the nodes and weights of a quadrature formula in such way that the values of a function are zero at all these nodes but one. With this representation the time required for calculating the Hamiltonian matrix elements is substantially reduced. The binding energies of several systems consisting of helium and lithium atoms have been obtained using the DVR method.