Interaction between light and hydrogen atom

[damosuz]

If a symmetric distribution of charge has no electric dipole moment, where does the $\mu$ term we write in the part of the hamiltonian representing interaction with light come from? We suppose it is induced by the electric field of the light?

 

[Jano L.]

The electric moment $\boldsymbol{\mu}$ used in the Hamiltonian operator is an operator as well - for hydrogen atom, $\boldsymbol \mu = e\mathbf r_p - e\mathbf r_e$. There is no symmetric charge distribution considered; the particles - electron and proton - are points whose possible configurations have generally non-zero electric moment.

When the $\psi$ function does not have special symmetry, the expected average value of electric moment

$$
\int \psi^* \boldsymbol{\mu} \psi\,d\tau
$$

may be non-zero as well.