Two Applications of the Variational Method to Quantum Mechanics

Walter Kohn

doi:10.1103/PhysRev.71.635

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Two Applications of the Variational Method to Quantum Mechanics

Walter Kohn^*

Department of Applied Mathematics, University of Toronto, Toronto, Canada

^*At present in the Department of Physics, Harvard University, Cambridge, Massachusetts.

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Phys. Rev. 71, 635 – Published 1 May, 1947

DOI: https://doi.org/10.1103/PhysRev.71.635

Abstract

By using the unperturbed wave function with a variable scale factor as trial-function for a perturbed Schroedinger equation, a lower bound for the second-order perturbation energy of the ground state in terms of the unperturbed and first-order perturbation energy is obtained. A minimum property of the sum of the $n$ lowest proper values is utilized in a new method for obtaining higher proper values and functions.

References (5)

Omitted endnote
A. Sommerfeld, Wave Mechanics (Methuen and Company, London, 1930) p. 248
E. A. Hylleraas, Zeits. f. Physik 60, 624 (1930)
E. A. Hylleraas and R. Undheim, Zeits. f. Physik 60, 759 (1930)
Courant-Hilbert, Meth. d. Math. Phys. (Verlagsbuch-handlung, Julius Springer, Berlin, 1931), second edition p. 399

[c1] Omitted endnote

[c2] A. Sommerfeld, Wave Mechanics (Methuen and Company, London, 1930) p. 248

[c3] E. A. Hylleraas, Zeits. f. Physik 60, 624 (1930)

[c4] E. A. Hylleraas and R. Undheim, Zeits. f. Physik 60, 759 (1930)

[c5] Courant-Hilbert, Meth. d. Math. Phys. (Verlagsbuch-handlung, Julius Springer, Berlin, 1931), second edition p. 399

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Two Applications of the Variational Method to Quantum Mechanics

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