tailieunhanh - Ideas of Quantum Chemistry P24

Ideas of Quantum Chemistry P24 shows how quantum mechanics is applied to chemistry to give it a theoretical foundation. The structure of the book (a TREE-form) emphasizes the logical relationships between various topics, facts and methods. It shows the reader which parts of the text are needed for understanding specific aspects of the subject matter. Interspersed throughout the text are short biographies of key scientists and their contributions to the development of the field. | 196 5. Two Fundamental Approximate Methods Hilbert space Appendix B p. 895 necessary . Matrix algebra Appendix A p. 889 needed . Lagrange multipliers Appendix N on p. 997 needed . Orthogonalization Appendix J p. 977 occasionally used . Matrix diagonalization Appendix K p. 982 needed . Group theory Appendix C p. 903 occasionally used in this chapter . Classical works The variational method of linear combinations of functions was formulated by Walther Ritz in a paper published in Zeitschrift für Reine und Angewandte Mathematik 135 1909 1. The method was applied by Erwin Schrödinger in his first works Quantisierung als Eigenwertproblem in Annalen der Physik 79 1926 361 ibid. 79 1926 489 ibid. 80 1926 437 ibid. 81 1926 109. Schrödinger also used the perturbational approach when developing the theoretical results of Lord Rayleigh for vibrating systems hence the often used term Rayleigh-Schrödinger perturbation theory . Egil Andersen Hylleraas in Zeitschrift der Physik 65 1930 209 showed for the first time that the variational principle may be used also for separate terms of the perturbational series. VARIATIONAL METHOD variational function VARIATIONAL PRINCIPLE Let us write the Hamiltonian H of the system under consideration1 and take an arbitrary variational function which satisfies the following conditions it depends on the same coordinates as the solution to the Schrodinger equation it is of class Q p. 73 which enables it to be normalized . We calculate the number e that depends on . e is a functional of e 1 M. The variational principle states e Eo where Eo is the ground-state energy of the system in the above inequality e Eq happens if and only if equals the exact ground-state wave function 0 of the system H q Eo o. 1We focus here on the non-relativistic case eq. where the lowest eigenvalue of 7 is bound from below -to . As we remember from Chapter 3 this is not fulfilled in the relativistic case Dirac s electronic sea and may lead to serious .