Let,s suppose we have a system [tex]H=H_{0}+\deltaH_{1}[/tex] where we know how to solve H0 to obtain its eigenfunctions and energies now let,s apply perturbation theory in the form:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]E_{n}=E^{0}_{n}+<\psi_0|\delta{H_{1}}|\psi_0>[/tex] but now we have that dH1 is so well behaved that gives us precisely the exact energies to first order in perturbation theory in the sense that [tex] <\psi_0|\delta{H_{1}}|\psi_0>=E_{n}-E^0_{N}[/tex] that is that the potential is given in a form that gives the exact energies to first order..but my question is if this would be possible and then what would happen to the rest terms in perturbation theory...thanx.

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# Exact perturbation

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