Nonperturbative methods in Quantum Mechanics of three or more particles

TL;DR

This paper reviews nonperturbative quantum mechanical methods applied to multi-particle systems, including atomic, molecular, and subatomic models, highlighting techniques and results from 1991 to 2005.

Contribution

It compiles and analyzes various nonperturbative methods used for three or more particle quantum systems, providing a comprehensive overview of theoretical approaches and their applications.

Findings

Exact diagonalization and analytical methods for small systems

Approximate methods like Monte Carlo and Hartree-Fock for larger systems

Computed properties include energy spectra, densities, and optical responses

Abstract

In the present report, a set of theoretical results obtained in the period from 1991 to 2005 are reviewed. The physical systems under study include quark models of hadrons, inert atom clusters, atomic traps, and electrons and excitons confined in quantum dots. They contain three or more particles, and are described by nonrelativistic Quantum Mechanics. In the smallest systems (6 particles or less), exact diagonalization complemented with the Lanczos algorithm, and some analytical approaches (1/D-expansion, improved semiclassical quantization, etc.) are used. In the larger systems (from 7 to hundreds of particles), we employ approximate methods, such as two-point Pade approximants, variational Monte Carlo estimations, Hartree - Fock and RPA schemes, BCS functions and the Bethe - Goldstone algorithm, etc. With the help of these methods, a variety of physical properties have been computed, i.e., energy spectra, particle densities, spin textures, light absorption and emission, inelastic light scattering, and some dynamical features.