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242 R. CARBÓ AND E. BESALÚ
The eigenvalues and eigenvectors of the unperturbed hamiltonian are assumed
to be known:
and the ket stands for the unperturbed eigenfunction of the i-th state and is the
corresponding energy. Also it is assumed that this system has an energy spectrum with
a simple structure.
The perturbed energies for the i-th state can be expressed as:
and the corresponding wavefunction is:
where the index n signals the correction order in expressions (34) and (35).
On the other hand, the n-th order energy correction can be written using the
form:
provided that the orthogonality condition holds between the unperturbed state
wavefunction and the corrections of any order:
where stands for a LKD.
5.4.1. Brillouin-Wigner perturbation theory
In the Brillouin-Wigner perturbation formalism, the following identity is used
[18]:
Combining equations (36) and (38) it can be easily found that the n-th order
wavefunction correction is given by [18]:
