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arXiv · 2206.05122

On the Rayleigh-Ritz variational method

Francisco M. Fernández
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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.

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Francisco M. Fernández. 2022-06-07. On the Rayleigh-Ritz variational method. https://arxiv.org/abs/2206.05122

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