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Perturbation theory refers to methods for understanding physical systems by treating them as small modifications to exactly solvable systems.
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What does it mean to expand a Hamiltonian using perturbation theory?
On UC Davis chemwiki website, the Hamiltonian for quadrupolar coupling in NMR is analyzed. (The details of this aren't important.)
It is said in the analysis that:
The expansion of the Hamiltoni …