Take the 2-minute tour ×  I'm studying the linear electric
susceptibility, using Schroedinger equation and perturbation
theory of the interaction potential  $$V=-\mu \cdot E$$  and the
book arrive to an expression where  $$\mu_{mn}=\langle
\psi_m\mid\hat\mu\mid\psi_n\rangle$$ is a "parameter" of the
problem.  My question is: which theory describes and calculates
$\hat\mu$?  share|improve this question What do you mean "which
theory describes" ? This is the standard electric dipole moment
in Electrodynamics. –  Chris Gerig Dec 6 '11 at 11:39 Ok, so you
are saying that I can use the multipolar expansion to explicitly
obtain $\mu$? –  J. C. Leitão Dec 6 '11 at 11:47  1 Answer 1  up
vote 1 down vote accepted  The idea is this. You will start from
an action in the form  $$S_I=\int d^4x j_\mu A^\mu$$  and for a
system of charge you will write down
$$j_\mu=(\rho(x),\rho(x)\dot{\bf x}).$$  An integration by part
in time will do the job producing the contribution  $$S'_I=-\int
d^4x \rho(x){\bf x}\cdot {\bf E}$$  usin