Đang chuẩn bị nút TẢI XUỐNG, xin hãy chờ
Tải xuống
Ideas of Quantum Chemistry P20 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. | 156 4. Exact Solutions - Our Beacons This result is exact for 0 E V . Despite its conciseness the formula for Dsingie as a function of E V looks quite complicated. What does this formula tell us Below are some questions Dsingle should increase when the particle energy E increases but is the function Dsingle E monotonic Maybe there are some magic energies at which passage through the barrier becomes easier Maybe this is what those guys in the movies use when they go through walls. The answer is given in Figs. 4.5.a-f. It has been assumed that the particle has the mass of an electron 1 a.u. . From Figs. 4.5.a-c for three barrier heights V it follows that the function is monotonic i.e. the faster the particle the easier it is to pass the barrier - quite a banal result. There are no magic energies. How does the function Dsingle V look with other parameters fixed For example whether it is easier to pass a low or a high barrier with the same energy or are there some magic barrier heights. Figs. 4.5.a-c tell us that at a fixed E it is easier to pass a lower barrier and the function is monotonic e.g. for E 0.5 a.u. 13.5 eV the transmission coefficient Dsingle is about 80 for V 0.5 40 for V 1 and 10 for V 2. No magic barrier heights. How does the transmission coefficient depend on the barrier width From Figs. 4.5.d-f we see that Dsingle a is also monotonic no magic barrier widths and dramatically drops when the barrier width a increases. On the other hand the larger the kinetic energy of the projectile heading towards the barrier the better the chance to cross the barrier. For example at electron energies of the order of 0.5 a.u. at fixed V 1 and m 1 the barrier of width 2 a.u. 1 A allows 6 of the particles to pass while at energy 0.75 a.u. 18 and at energy 1 a.u. 30 pass. What does the wave function of the tunnelling particle look like The answer is in Fig. 4.6. We see that The real as well as the imaginary parts of the wave function are non-zero in the barrier i.e. the .
