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<p>We apply the well known Rayleigh–Ritz method (RRM) to the projection of a Hamiltonian operator chosen recently for the extension of the Rayleigh–Ritz variational principle to ensemble states. By means of a toy model we show that the RRM eigenvalues approach to those of the projected Hamiltonian from below in most cases. We also discuss the effect of an energy shift and the projection of the identity operator.</p>

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On the application of the Rayleigh–Ritz method to a projected Hamiltonian

  • 期刊论文

  • 发表日期：

    2025年4月10日

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  • Francisco M. Fernández

摘要

We apply the well known Rayleigh–Ritz method (RRM) to the projection of a Hamiltonian operator chosen recently for the extension of the Rayleigh–Ritz variational principle to ensemble states. By means of a toy model we show that the RRM eigenvalues approach to those of the projected Hamiltonian from below in most cases. We also discuss the effect of an energy shift and the projection of the identity operator.