# Interaction between light and hydrogen atom

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?

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Jano L.
Gold Member
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.