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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.
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Cited by 1 Pith paper
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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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