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On the Rayleigh-Ritz variational method
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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.
Forward citations
Cited by 2 Pith papers
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On the application of the Rayleigh-Ritz method to a projected Hamiltonian
For a particle-in-a-box toy model, Rayleigh-Ritz eigenvalues for a projected Hamiltonian converge from below (mostly), unlike the usual upper-bound behavior, with exact zero eigenvalues for the null space.
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On the exact solutions of a two-dimensional hydrogen atom in a constant magnetic field
The polynomial quasi-exact solutions for the 2D hydrogen atom in a magnetic field match true eigenstates only at special field strengths, so they are not the full spectrum.
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