we shall describe a simple model for a linear molecule, say, CO2.
the states |L>, |C>,|R> are the eigenstates of D operator (corresponds to dipole moment)
D|L>=-d|L> , D|C>=0 , D|R>= +d|R>.
When the electron is localized exactly on the carbon atom, its energy is E1 and
when it is localized on one of the oxygen atoms, it has energy E0 ( assuming
E1 > E0). In addition, the electron can "jump" from one atom to another, and
this jump is characterized by kinetic energy a. We can assume that the jumping
occurs only between nearest neighbors.
Write matrix representation of the Hamiltonian in the basis of |L>, |C>,|R>.
2. The attempt at a solution
we should build the matrix from the matrix elements - <L|H|L>, <L|H|C> etc.
the matrix should look like that:
E0 a 0
a E1 a
0 a E0
it seems very logical, but I still don't see the direct connection between the matrix elements and the given data. for example, why does the element <L|H|L> equals E0?
what does the element <1|H|2> mean in general?