English

On the Rayleigh-Ritz variational method

Quantum Physics 2023-11-07 v4

Abstract

We give a simple proof of the well known fact that the approximate eigenvalues provided by the Rayleigh-Ritz variational method are increasingly accurate upper bounds to the exact ones. To this end, we resort to the variational principle, mentioned in most textbooks on quantum chemistry, and to a well known set of projection operators. We think that present approach may be suitable for an advanced course on quantum mechanics or quantum chemistry.

Keywords

Cite

@article{arxiv.2206.05122,
  title  = {On the Rayleigh-Ritz variational method},
  author = {Francisco M. Fernández},
  journal= {arXiv preprint arXiv:2206.05122},
  year   = {2023}
}
R2 v1 2026-06-24T11:46:38.071Z