Diagonalization scheme for the many-body Schroedinger equation

TL;DR

This paper introduces a novel diagonalization method for the many-body Schrödinger equation that simplifies calculations by combining kinematic rotations and exact overlap integrals, validated on the three-body Calogero model.

Contribution

The paper presents a new diagonalization scheme that efficiently handles many-body problems with two-body potentials by integrating kinematic rotations and exact integral calculations.

Findings

Accurately diagonalizes the three-body Calogero model

Simplifies the solution of many-body Schrödinger equations

Provides a validated method for complex quantum systems

Abstract

A new convenient method to diagonalize the non-relativistic many-body Schroedinger equation with two-body central potentials is derived. It combines kinematic rotations (democracy transformations) and exact calculation of overlap integrals between bases with different sets of mass-scaled Jacobi coordinates, thereby allowing for a great simplification of this formidable problem. We validate our method by obtaining a perfect correspondence with the exactly solvable three-body ($N=3$) Calogero model in 1D.