2nd Order Perturbation Coefficients.

[Morberticus]

I have found an expression for the estimated energy contribution a term |I> will bring to a wavefunction |K>

\Delta E = \frac{|\langle I|\hat{H}| K\rangle|^2}{(E_K - \langle I |\hat{H}| I\rangle)}

Is there a simple way to extract the coefficient that will be associated with |I>? Even a link to relevant literature would be appreciated.

Thanks

 

[DrDu]

The first order correction to the wavefunction k reads something like
$|k\rangle_1=|k\rangle+\sum_I\frac{\langle I|H| k\rangle}{E_k-\langle I|H|I \rangle } |I\rangle$
using your notation. It is enough to calculate the second order correction to energy.
Is it that what you are looking for?
Any book on QM will contain a chapter on perturbation theory.
Also wikipedi contains quite a lot:
http://en.wikipedia.org/wiki/Perturbation_theory_(quantum_mechanics)