tailieunhanh - Ideas of Quantum Chemistry P49

Ideas of Quantum Chemistry P49 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. | 446 9. Electronic Motion in the Mean Field Periodic Systems the levels extend over an energy interval and are more numerous at energy extremes. How do the wave functions that correspond to higher and higher-energy levels in a band look Let us see the situation in the ring Hn molecules. Fig. indicates that the rule is very simple. The number of nodes of the wave function increases by one when we go to the next level higher in the energy scale .19 Born-von Karman condition in 1D How is it in the case of a crystal Here we are confronted with the first difficulty. Which crystal of what shape Should it be an ideal crystal . with perfectly ordered atoms There is nothing like the perfect crystal in Nature. For the sake of simplicity as well as generality let us assume however that our crystal is perfect indeed. Well and now what about its surface shape Even if we aimed at studying the surface of a crystal the first step would be the infinite crystal . with no surface . This is the way theoreticians always One of the ingenious ideas in this direction is known as the Born-von Karman boundary conditions. The idea is that instead of considering a crystal treated as a stick let us consider 1D case we treat it as a circle . the value of the wavefunction at one end of the stick has to be equal to the wavefunction value at the other end. In this way we remove the problem of the crystal ends and on top of that all the unit cells become equivalent. Theodore von Karman 1881-1963 American physicist of Hungarian origin director of the Guggenheim Aeronautical Laboratory at the California Institute of Technology in Pasadena. von Karman was also a founder of the NASA Jet Propulsion Laboratory and father of the concept of the first supersonic aeroplane. On the Hungarian stamp one can see the famous Karman vortex street behind an aeroplane. He was asked by the father of the young mathematical genius John von Neumann to persuade him that the job of a mathematician is