L7_Chap3英文版原子物理课件.pptVIP

3.3 Evaluation of the integrals in helium 3.3.1 Ground State_1 3.3.1 Ground State_2 3.3.1 Ground State_3 3.3.2 Excited states: the direct integral_1 3.3.2 Excited states: the direct integral_2 3.3.2 Excited states: the direct integral_3 3.3.2 Excited states: the direct integral_4 3.3.2 Excited states: the direct integral_5 3.3.3 Excited states: the exchange integral_1 3.3.3 Excited states: the exchange integral_2 3.3.3 Excited states: the exchange integral_3 3.3.3 Excited states: the exchange integral_4 Exercises * *Shanxi University Atomic Physics Calculating the direct and exchange integrals to make quantitative predictions for some of the energy levels in the helium atom, based on the theory described in the previous sections. This provides an example of the use of atomic wavefunctions to carry out a calculation where there are no corresponding classical orbits and gives an indication of the complexities that arise in systems with more than one electron.. The important point to be learnt from this section, however, is not the mathematical techniques but rather to see that the integrals arise from the Coulomb interaction between electrons treated by straightforward quantum mechanics. To calculate the energy of the 1s2 configuration we need to find the expectation value of e2/4??0r12 in eqn 3.1—this calculation is the same as the evaluation of the mutual repulsion between two charge distributions in classical electrostatics, as in eqn3.15 with ?1s(r1) and ?nl(r2) = ?1s(r2). The integral can be considered in different ways. We could calculate the energy of the charge distribution of electron 1 in the potential created by electron 2, or the other way around. This section does neither; it uses a method that treats each electron symmetrically (as in Appendix B), but of course each approach gives the same numerical result. Electron 1 produces an electrostatic potential at radial distance r2 given by