Improvement of the Envelope Theory for Systems with Different Particles

TL;DR

This paper enhances the envelope theory for quantum N-body systems by integrating a generalized orbital state method, improving eigenvalue accuracy for systems with identical and different particles.

Contribution

It introduces a novel improvement to the envelope theory applicable to systems with mixed particle types, extending previous methods for better eigenvalue approximations.

Findings

Improved eigenvalue accuracy for systems with identical particles.

Effective extension of the method to systems with different particles.

Validated the approach with various quantum systems.

Abstract

The envelope theory is a method to compute approximate eigensolutions of quantum $N$-body Hamiltonians with a quite general structure in $D$ dimensions. The advantages of the method are that it is easy to implement and that $N$ is treated as any other parameters of the Hamiltonian, allowing the computation for systems of all sizes. If solutions are reliable, they are generally not very accurate. In the case of systems with identical particles for $D \ge 2$, it is possible to improve the precision of the eigenvalues by combining the envelope theory with a generalisation to $N$-body of the dominantly orbital state method. It is shown that a similar improvement can be achieved in the case of systems composed of identical particles plus a different one. The quality of the new procedure is tested with different systems.