Intuitions on perturbation theory?
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●1st order energy correction can be calculated using only zeroth order wavefunctions This point can be quite natural, but if you see '2n+1 theorem' in perturbation theory...
●'2n+1 theorem' states that by using only 1~nth order wavefunctions, you can calculate up to (2n+1)th order energy correction. I tried to understand this by gauge restrictions(I don't know if its right expression... what I mean is just counting the number of constraints like orthonormalization of zeroth order wf, orthogonality of zeroth and first order wf...) Actually, 1 is the special(and simpliest) case of 2.
●What's more peculiar is this. Time dependent perturbation theory states that when you integrate nth order wavefunction correction, you can get (n+1)th order wavefunction correction.
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●'2n+1 theorem' states that by using only 1~nth order wavefunctions, you can calculate up to (2n+1)th order energy correction. I tried to understand this by gauge restrictions(I don't know if its right expression... what I mean is just counting the number of constraints like orthonormalization of zeroth order wf, orthogonality of zeroth and first order wf...) Actually, 1 is the special(and simpliest) case of 2.
●What's more peculiar is this. Time dependent perturbation theory states that when you integrate nth order wavefunction correction, you can get (n+1)th order wavefunction correction.
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☞ I'd say perturbation theory is a generalisation of several mathematical tools you find in different fields -- e.g. Taylor series, momentary expansions of statistical variables, Fourier series and in general any convergent infinite sum. With the specific case of kernel perturbations, you can consider each perturbation to the kernel to be a result of a scattering process that affects the Lagrangian in some way...
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