- In a diagonalizing basis
**e**_{i'}our equation looks as follows:

(3.56)

where a bracketed index implies that there is no summation. The solution is, for every*l*':

(3.57)

- In order to obtain a solution in terms of
*a*^{l}(*t*) we simply need to rotate the basis back to the original one:

*a*^{l}(*t*)= = = (3.58)

The presence of between the two big lambdas implies that we cannot simply contract and get Kronecker delta. The evolution of the system derives from those terms .