Approximate solutions for N-body Hamiltonians with identical particles in D dimensions

TL;DR

This paper introduces an envelope theory-based method to approximate solutions for N-body Hamiltonians with identical particles in D dimensions, providing analytical bounds and applications to systems with minimal length.

Contribution

It presents a novel envelope theory approach for N-body problems in higher dimensions, enabling analytical bounds and semiclassical interpretations.

Findings

Analytical bounds for eigenvalues in favorable cases

Application to N-body systems with minimal length

Semiclassical interpretation of eigenvalue formulas

Abstract

A method based on the envelope theory is presented to compute approximate solutions for $N$-body Hamiltonians with identical particles in $D$ dimensions ($D\ge 2$). In some favorable cases, the approximate eigenvalues can be analytically determined and can be lower or upper bounds. An application to a $N$-body system with a minimal length is studied, and a semiclassical interpretation of the generic formula obtained for the eigenvalues is given.