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Erratum: Lattice Dynamics of Cubic Lattices with Long‐Range Interactions
1.P. Noziéres and D. Pines, Nuovo Cimento 9, 470 (1958);
1.see also M. Born and P. Jordan, Elementare Quantenmechanik (Springer‐Verlag, Berlin, 1930), pp. 236ff.
2.For a critique of the conventional time‐dependent perturbation theory, see J. H. Shirley, Ph.D. thesis, California Institute of Technology, 1963.
3.R. H. Young, W. J. Deal, Jr., and N. R. Kestner, Mol. Phys. 17, 369 (1969).
4.J. H. Shirley, Phys. Rev. 138, B979 (1965).
5.R. H. Young and W. J. Deal, Jr., Phys. Rev. A 1, 419 (1970).
6.Here convergence in the mean is used in the definitions of continuity and differentiation.
7.See, for instance, M. H. Stone, Linear Transformations in Hilbert Space (American Mathematical Society, New York, 1966), p. 30.
8.Reference 7, p. 128.
9.S. Lefschetz, Differential Equations: Geometric Theory (Interscience, New York, 1963), p. 44.
10.T. Kato, Perturbation Theory for Linear Operators (Springer, New York, 1966), pp. 71, 99–102;
10.for a simpler treatment which can be adapted, see F. Rellich, Math. Ann. (Leipzig) 113, 600 (1939).
11.Ralph H. Young, Ph.D. thesis, Stanford University, 1968.
12.Sufficient conditions for the existence and convergence of the Rayleigh‐Schrödinger theory are well known.
12.See, for instance, T. Kato, J. Fac. Sci., Univ. Tokyo, Sect. I, 6, 145 (1949).
13.E. Wigner, Group Theory (Academic, New York, 1959), p. 26.
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