In chapter nine of Griffiths' Quatum Mechanics text, he talks about the method of succesive approximations as a method for solving a two level system in time dependent perturbation theory.(adsbygoogle = window.adsbygoogle || []).push({});

d(ca)/dt = f(t) cb --> ca_n = int[ f(t') * cb_n-1, dt', 0 t]

d(cb)/dt = g(t) ca --> cb_n = int[ g(t') * ca_n-1, dt', 0 t]

So, for the case were ca(0) = 1 and cb(0) = 0 one would get:

ca1 = int [f(t') * 0, dt', 0, t] = 0

cb1 = int [g(t') * 1, dt', 0, t]

but griffiths says ca1 = 1.

So, my question is the following. Is ca = ca_0 + ca_1 + ca_2 + ...

or, is ca ~ ca_n (with larger n being more precise)?

I hope my question was clear. I should really learn LATEX.

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# Homework Help: Time dependent perturbations and method of succesive approximations

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