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.