Chemistry Reference
In-Depth Information
10
Elements of Rayleigh-
Schroedinger Perturbation
Theory
In this chapter we present a few elements of RS stationary perturbation
theory, where a stationary system acted upon by an external perturbation
will change by a small amount its energy levels and eigenstates. It consists
essentially in relating the actual eigenvalue problem to be solved to one for
which a complete solution is exactly known, and in treating the difference
between the two Hamiltonian operators as a small perturbation.
10.1 RAYLEIGH-SCHROEDINGER PERTURBATION
EQUATIONS UP TO THIRD ORDER
We want to solve the Schroedinger eigenvalue equation
ð
H
E
Þc ¼
0
ð
10
:
1
Þ
for a Hermitian decomposition of the Hamiltonian H into:
H
¼
H
0
þ
l H
1
ð
10
:
2
Þ
is a parameter giving the orders in perturbation theory,
1
(ii) H
0
is the unperturbed Hamiltonian, namely the Hamiltonian of an already
where (i)
l
1
Orders are here carried by the suffixes or their sum.
