- #1

Phylosopher

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- TL;DR Summary
- Why do we use power series in perturbation theory? What is its mathematical justification?

I am revising perturbation theory from Griffiths introduction to quantum mechanics.

Griffiths uses power series to represent the perturbation in the system due to small change in the Hamiltonian. But I see no justification for it! Other than the fact that it works.

I searched on the internet a bit, but I saw no digestible answer.

This: Ref1, Ref2 are good to read, but they do not answer why use a power series to begin with.

Interestingly, Ref2 uses perturbation on a simple algebraic equation and claims at the end that "regular" perturbation cannot generate all the possible answers.

Griffiths uses power series to represent the perturbation in the system due to small change in the Hamiltonian. But I see no justification for it! Other than the fact that it works.

I searched on the internet a bit, but I saw no digestible answer.

This: Ref1, Ref2 are good to read, but they do not answer why use a power series to begin with.

Interestingly, Ref2 uses perturbation on a simple algebraic equation and claims at the end that "regular" perturbation cannot generate all the possible answers.