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

Time-independent, non-degenerate perturbation theory:

- Let |k> represent k-th order wave function correction.

- Let [itex]E^{(k)}[/itex] represent k-th order energy correction

- H' is the perturbed Hamiltonian.

Want the third order energy correction:

[tex]E^{(3)} = <1|H' - E^{(1)}|1> - 2E^{(2)}<0|1>[/tex]

2. Relevant equations

Equating coefficients of equal powers of the parameter:

[tex]H_0|3> + H'|2> = E^{(0)}|3> + E^{(1)}|2> + E^{(2)}|1> + E^{(3)}|0>[/tex]

3. The attempt at a solution

Tried multiplying <0| on the left like when deriving the first order correction, [itex]E^{(1)}[/itex].

I get,

[tex]E^{(3)} = <0|H' - E^{(1)}|2>[/tex]

I don't know what I'm missing to proceed... I'm in the same situation with a few other similar problems. I don't see how multiplying by anything else on the left would make sense either.

Hint on what I'm missing? Thanks

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# Homework Help: 3rd-order Energy Correction Derivation

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