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Definitive variational principles for physical quantities

I. Extremal features of functionals bilinear relative to the hamiltonian: Definitive variational principles for the polarizability and related quantities

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Abstract

A functional of general form is examined, which is bilinear with respect to the Hamiltonian. It is shown that choice of the coefficients in the functional gives the stationary value as an infinite sum having the structure of the infinite sums of perturbation theory. The conditions for definitiveness of the corresponding variational principles are established. The general theory is applied to obtain new definitive variational principles expressing the dynamic polarizability of a quantum-mechanical system (with or without allowance for damping) in the form of variational problems for maxima and minima. Analogous variational problems are formulated for the energy of the dispersion interaction of two atoms or molecules.

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Authors
  1. P. A. Braun
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  2. T. K. Rebane
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Additional information

The principal results in this paper have been reported at the Fourth All-Union Conference on Quantum Chemistry [6].

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Braun, P.A., Rebane, T.K. Definitive variational principles for physical quantities. Theor Exp Chem 3, 479–482 (1971). https://doi.org/10.1007/BF00523712

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  • DOI: https://doi.org/10.1007/BF00523712

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