(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

In each of my QM books, they always say something like "we can write the perturbed energies and wavefunctions as"

[tex]E_n = E_n^{(0)} + \lambda E_n^{(1)} + \lambda^2 E_n^{(2)} + \cdots [/tex]

[tex] |n\rangle = |n^{(0)}\rangle + \lambda |n^{(1)}\rangle + \lambda^2 |n^{(2)}\rangle + \cdots [/tex]

without any justification. This is really not obvious to me and although it seems reasonable, it do not see why the perturbed energies and wavefunctions might not be something completely different like

[tex]E_n = E_n^{(0)} + \lambda E_n^{(1)} + \lambda^2 \log \left(E_n^{(2)}\right)^{-1}\sin E_n^{(2)} + \cdots [/tex]

[tex] |n\rangle = |n^{(0)}\rangle + \lambda |n^{(1)}\rangle + \lambda^2 |n^{(2)}\rangle + \cdots [/tex]

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Time-independent perturbation theory

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