For $x$ and $x^2$ we get exact solution easily without applying perturbation theory, but I read that above order perturbation can not be solved exactly. Can anyone explain clearly why?
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RISHAV SAGAR
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1why would you expect an exact solution in terms of "simple" functions? Plenty of differential equations (in fact the majority of differential equations) do not have solutions expressible in terms of such "elementary" functions. – ZeroTheHero Mar 05 '20 at 14:14
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Related: How to obtain large order perturbation series for cubic anharmonic oscillator? – Qmechanic Nov 29 '22 at 15:32