Theorems of Quantum Mechanics, Study notes of Quantum Chemistry

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Theorems of Quantum Vechanics .1 Introduction The Schroedinger equation for the one-electron atom (Chapter 6) and 1e electronic Schroedinger equation for the one-electron diatomic mole- ale (Section 13.3) are exactly soluble; however, because of the inter- ‘eetronic repulsion terms in the Hamiltonian, the Schroedinger equation o many-electron atoms and molecules is not separable in any coordinate ‘stem, and cannot be solved exactly, Hence, we must seek approximate sethods of solution. The two main approximation methods, the variation sethod and perturbation theory, will be developed in Chapters 8 and 9; » derive these methods, we must develop further the theory of quantum iechanics, which is what we will do in this chapter. Although much of the ork will be of an abstract nature, and perhaps not so easy to master, the eorems we will derive are basic to an understanding of quantum vechanics. We will conclude this chapter with a summary of the postulates of uantum mechanics. 2 Notation Before getting started, we introduce some notations for the integrals ‘ith which we will be dealing. These notations are in widespread use, and is helpful to be familiar with them, 144