hi there; I need some help with the following formulas(adsbygoogle = window.adsbygoogle || []).push({});

In the interaction picture.

##\frac{d}{dt}\rho(t)=\frac{1}{i\hbar}[V(t),\rho(t)]## (1)

Then

##\rho(t+\Delta t) = \rho(t)+\frac{1}{i\hbar}\int_t^{t+\Delta t} dt' [V(t'),\rho(t')]## (2)

This equation can be iterated. and it is

##\Delta \rho(t)=\frac{1}{i\hbar}\int_t^{t+\Delta t} dt' [V(t'),\rho(t')]+(\frac{1}{i\hbar})^2 \int_t^{t+\Delta t} dt' \int_t^{t'}dt''[\underbrace{V(t'),[V(t'')}_{Note\;t'\;and\;t''},\rho(t'')]]## (3)

##\Delta \rho(t) = \rho(t+\Delta t) - \rho(t)##

I can understand the eq.(2), but not the eq. (3).

Is anybody know how to get the equation (3). and why do we want to do such calculation?

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# Iteration method for density equations

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