Abstract
Explicit equations are obtained which define the derivatives with respect to parameters entering in the Hamiltonian of the eigenvalues of the Hamiltonian (through third order in the degenerate and nondegenerate cases). A method is indicated of introducing a basis depending on the parameters. A compact expression is obtained for the correction of arbitrary order to the energy in the Rayleigh-Schrodinger perturbation theory.
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A. Ya. Tsaune, Izv. VUZ. Fiz., No. 3, 74 (1971).
N. I. Akhiezer and I. M. Glazman, Theory of Linear Operators in Hubert Space [in Russian], Nauka, Moscow (1966).
W. R. Salzman, J. Chem. Phys.,49, No. 7, 3035 (1968).
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 3, pp. 72–75, March, 1972.
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Tsaune, A.Y. Derivatives of the hamiltonian eigenvalues with respect to parameters. Soviet Physics Journal 15, 366–368 (1972). https://doi.org/10.1007/BF00834598
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DOI: https://doi.org/10.1007/BF00834598