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

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.