When we have
established the molecular orbital energies E1
and E2, we can go back to
the secular equations and insert, in turn, each of the energies.
· The equations
now have non-trivial solutions.
· Solving the
equations gives us THE RATIO ci1/ci2.
We must still normalize the MOs, using the normalization
condition:
From this,
Ş 
Since we know the ratio of the coefficients 
, this extra condition of normalization fixes the values
of the coefficients absolutely.