The few-body problem in terms of correlated gaussians

TL;DR

This paper derives new formulas for correlated Gaussian bases, including Fourier transforms and relativistic kinetic energy applications, enhancing the efficiency of calculations in quantum few-body problems.

Contribution

It introduces novel, more efficient formulations for correlated Gaussian matrix elements, including Fourier transforms and relativistic kinetic energy operators, filling gaps in existing literature.

Findings

Derived Fourier transform formulas for correlated Gaussians

Presented efficient formulations for relativistic kinetic energy

Enhanced numerical efficiency for central potential calculations

Abstract

In their textbook, Suzuki and Varga [Y. Suzuki and K. Varga, {\em Stochastic Variational Approach to Quantum-Mechanical Few-Body Problems} (Springer, Berlin, 1998)] present the stochastic variational method in a very exhaustive way. In this framework, the so-called correlated gaussian bases are often employed. General formulae for the matrix elements of various operators can be found in the textbook. However the Fourier transform of correlated gaussians and their application to the management of a relativistic kinetic energy operator are missing and cannot be found in the literature. In this paper we present these interesting formulae. We give also a derivation for new formulations concerning central potentials; the corresponding formulae are more efficient numerically than those presented in the textbook.