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Diagrammatical Derivation and Representation of Rayleigh–Schrödinger Perturbation Theory
1.H. Eyring, J. Walter, and G. E. Kimball, Quantum Chemistry (John Wiley & Sons, Inc., New York, 1944), pp. 92–98.
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3.The sense in which V is small is usually taken to be that for two eigenvectors of and . This condition of course does not hold if and are degenerate and in which case special precautions are necessary. See Ref. 1.
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7.See, for example, J. E. Mayer in Encyclopedia of Physics, S. Flügge, Ed. (Springer‐Verlag, Berlin, 1958), Vol. 12, p. 73.
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11.A. Messiah, Quantum Mechanics, translated by J. Potter (North‐Holland Publ. Co., Amsterdam, 1962), Vol. 2, p. 686.
12.D. J. Thouless, The Quantum Mechanics of Many‐Body Systems (Academic Press Inc., New York, 1961), p. 33.
13.If necessary, the energy levels may be made discrete by enclosing the system in a large box.
14.See, for example, P.‐O. Löwdin, J. Math. Phys. 3, 969 (1962).
15.R and are true projection operators with and but i.e., is not idempotent
16.P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw‐Hill Book Co., New York, 1953), Pt. 2, p. 1001.
17.Strictly speaking, the quantities we are referring to as matrix elements of are expectation values for the state of some operator.
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