Abstract
A method is described for finding the first- and higher-order derivatives of the eigenvectors of a Hamiltonian with respect to its parameters. This method is useful even when the explicit dependence of the eigenvectors on the parameters is not known. The method is based on a transfer of the differentiation from the eigenvector to the Hamiltonian and on a separate analysis of the derivatives of the projections of the eigenvector onto the corresponding subspace and onto the orthogonal complement of this subspace. Conditions governing the position of the eigenvector being differentiated in its degenerate subspace are analyzed. This method can be used in certain fundamental problems, and it can be related to steady-state Rayleigh-Schrö-dinger perturbation theory.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Literature cited
N. I. Akhiezer and I. M. Glazman, Theory of Linear Operators in Hilbert Space [in Russian], Nauka, Moscow (1966).
B. W. Brown, Proc. Camb. Phil. Soc.,58, 251 (1958).
J. C. Y. Chen, J. Chem. Phys.,38, No. 1, 283 (1963).
L. Schiff, Quantum Mechanics, McGraw-Hill, New York (1968).
L. Salem, Phys. Rev.,125, 1788 (1962).
Author information
Authors and Affiliations
Additional information
Translated from Izvestiya Vysshikh Uchebnykh Zave-denii Fizika, No. 3, pp. 74–78, March, 1971.
Rights and permissions
About this article
Cite this article
Tsaune, A.Y. Derivatives with respect to parameters of the eigenvectors of a Hamiltonian and their application. Soviet Physics Journal 14, 348–351 (1971). https://doi.org/10.1007/BF00822268
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00822268