By Stuart A Rice; I Prigogine
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10). Eqs. (46) and (47) must be solved simultaneously or iteratively. In analogy with the variational principle of HulthCn,s7 the trial function \Ti can be required to satisfy the condition that the functional (Ti,(H- E)YJ should vanish. Since Eqs. (46) are already required to be satisfied, this is equivalent to requiring that ( W , ( H - E ) Y J= 0 (49) Eq. (49) also follows from Eq. (47). When expressed in terms of matrix elements, Eq. (49) becomes a formula for the parameter E , E - Hm = &k f (klk)-'z(ikIRld)< ab (50) Here &k is the Hartree-Fock energy of the continuum orbital, &kain atomic units.
83 hppendix : Proof of Auxiliary Theorems of Section 3 . Acknowledgements . a7 References . 88 1. Introduction 2. 3. 4. 5. 6. Pz 35 36 JIMCEEK 1. INTRODUCTION A. 2 The aim of this article is to show how the mathematical methods of quantum-field theory may be used to calculate the wave function describing the non-degenerate ground state of an atomic or molecular system as well as to calculate the mean value of an arbitrary operator. We shall be mainly concerned with the mathematics of this problem, while the possible use of this methodology for the reformulation or even unification of the former theories will only be sketched out.
Normally, one assigns to a diagram a simple product of creation and annihilation operators while here a normal product J Fig. 4. A general S,(j) skeleton. of the same operators is attributed to it. The latter assignment is usually employed in quantum electrodynamics, too (cf. Reference 3a). . Usually the scalar quantity -(C,1t21B1) is attributed to the H diagram of the second type while here we assign to it the scalar quantity