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Ideas of Quantum Chemistry P12

Ideas of Quantum Chemistry P12 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. | 76 2. The Schrôdinger Equation dynamical symmetry one may obtain an accidental degeneracy which does not follow from the symmetry of an object like a chair but from the properties of the potential field and is called dynamical symmetry 3 - the chair is in the normal position E3 1. There are no more stable states of the chair23 24 and there are only four energy levels Fig. 2.6. The stable states of the chair are analogues to the stationary quantum states of Fig. 1.8.b d on p. 23 while unstable states of the chair on the floor are analogues of the non-stationary states of Fig. 1.8.a c. 2.2.4 MATHEMATICAL AND PHYSICAL SOLUTIONS It is worth noting that not all solutions of the Schrodinger equation are physically acceptable. underground states For example for bound states all solutions other than those of class Q see p. 895 must be rejected. In addition these solutions which do not exhibit the proper symmetry even if 2 does have also to be rejected. They are called mathematical non-physical solutions to the Schrodinger equation. Sometimes such mathematical solutions correspond to a lower energy than any physically acceptable energy known as underground states . In particular such illegal non-acceptable functions are asymmetric with respect to the label exchange for electrons e.g. symmetric for some pairs and antisymmetric for others . Also a fully symmetric function would also be such a non-physical purely mathematical solution. 2.3 THE TIME-DEPENDENT SCHRODINGER EQUATION What would happen if one prepared the system in a given state which does not represent a stationary state For example one may deform a molecule by using an electric field and then switch the field off.25 The molecule will suddenly turn out to be in state that is not its stationary state. Then according to quantum mechanics the state of the molecule will start to change according to the time evolution equation time-dependent Schrodinger equation H ih dt. 2.13 23Cf. the original works C. Runge .