Hi all. I m stucked on the question followed, any helps will be greatly appreciated.(adsbygoogle = window.adsbygoogle || []).push({});

A perturbation has the form H^{'}=z act on a two level system which they have different parity.

So the first order correction to the energy level 1 and 2 are give by:

E_{1}^{1}=<ψ_{1}| H^{'}|ψ_{1}>

Same for level 2.

These two energy correction are clearly zero because the same level has same parity.

However the first order wavefunction corrections are not for both level:

According to time independent non-degenerate perturbation theory on the 1st order correction to the wave function formula:

ψ_{1}^{1}=<ψ_{2}| H^{'}| ψ_{1}>/(E_{1}-E_{2}) ψ_{2}

Which is none zero

Where am I wrong? I am so confused..thanks in advance.

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# 1st order pertubation on 2 level system

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