By Stuart A Rice; I Prigogine

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Wick’s Theorem and Contractions . 44 Introduction to “Graphology” . 46 A. General Remarks . 46 B. Definition and Properties of Skeletons . 47 . 49 C. N, T , and M Skeletons and Diagrams . 54 Equations for Matrix Elements of the Operator f? A. Formulation of Auxiliary Theorems . 54 . 57 B. Transformation of the Schriidinger Equation . C. Explicit Form of the Equations for Matrix Elements of the . 59 Operator 9. in the Approximation f’ The Evaluation of the Mean Values of One- and Two-Particle .

11). If the continuum orbital were normalized to make ( $ k , $ k ) equal unity the integrated electronic density within any finite region would vanish, and there is no self-consistent effect of the external particle on the occupied bound state orbitals di, i 5 N . The function $k, for wave number k. For consistency with earlier notation, the symbol det in Eq. )-* times the antisymmetrizing operator. The first-order Bethe-Goldstone equation with index i, for elastic scattering of a single external particle, is equivalent to a variational calculation with a trial function of the form $k \Ti= Q k + paby b c c " (44) The notation consistent with that used in Section 2, above, describes an ( N $- 1)-particle Slater determinant in terms of an N-particle reference state.

Final Expression for Mean Values . Final Remarks . 75 -4. Relationship to Former Theories . 75 B. Actual Calculations . 76 . 82 C. On a Generalization of the Theory Presented . . 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.