现代物理前言 第5章.ppt

To be very explicit, the hamiltonian for 1,3-butadience would be written (6.5.9) This hamiltonian is written in the representation of basis functions;as such it is not Diagonal. We wish,in general,to rewrite the hamiltonian in diagonal form. To do so,we define a new set of orbitals as (6.5.10) with arbitrary coefficients ;the are molecular orbitals,and this expansion represents the usual LCAO-MO form. We wish to find the expansion coefficients and the MO energies To do so,we use the fact that the Mos are eigenstates of the one-electron hamiltonian H,and write (6.5.11) Then we express the MO as a one-electron function (6.5.12) with the vacuum state containing no electrons, and with the spin index suppressed for clarity. Using the hamiltonian form of (6.5.3),we find, from (6.5.10), (6.5.13) Now we define the creation operator for the Mos by (6.5.14) with Greek Subscripts labeling Mos and Latin subscripts labeling Aos. For real Mos,the complex conjugate can be igored. Then (6.5.11) becomes (6.5.15) Now we take the matrix element with the occupied one-electron atomic basis function (6.5.16) Now using the identity and the anticommutation relations (6.3.2),we have