A variant of the Brillouin-Wigner perturbation theory with Epstein-Nesbet partitioning

TL;DR

This paper introduces a simplified variant of the Brillouin-Wigner perturbation theory with Epstein-Nesbet partitioning, enabling efficient higher-order calculations and demonstrating accuracy on basic quantum systems.

Contribution

It presents a new, easily extendable variant of the Brillouin-Wigner perturbation theory that reduces computational effort for higher orders.

Findings

The new theory accurately predicts energies of simple quantum systems.

Computational time for higher-order results is negligible after third order.

The approach is suitable for quasi-degenerate systems.

Abstract

We present an elementary pedagogical derivation of the Brillouin-Wigner and the Rayleigh-Schr\"odinger perturbation theories with Epstein-Nesbet partitioning. A variant of the Brillouin-Wigner perturbation theory is also introduced, which can be easily extended to the quasi-degenerate case. A main advantage of the new theory is that the computing time required for obtaining the successive higher-order results is negligible after the third-order calculation. We illustrate the accuracy of the new perturbation theory for some simple model systems like the perturbed harmonic oscillator and the particle in a box.