# Transition dipole -- Line shape function

1. May 2, 2015

### Goodver

I am confused with the classical approach of usage of a "transition dipole oscillation" in order to explain the broadening of spectrum of emission between energy levels.

1. If I understand it correctly then emission of photon is due to oscillation of a dipole consisting of an electron-proton pair, right? In this case, electrons just oscillate on orbitals but do not change their orbitals? Or electrons also jump to the higher and lower orbitals? If they change, then electron oscillates on its way from one orbital to another?

2. Lifetime defined as a time until electron oscillation gets damped, but electron stay on its orbital or time takes for electron to transit from one orbital to another? What determines the different lifetimes for different atoms?

3. Why broadening of a spectrum can not be explain with a solid state physics concept of Kronig-Penney model, where we have bands instead of level in a multi atomic system?

4. Why dipole can oscillates only with a frequency corresponding to the energy difference between energy levels?

Picture taken from this thread:

Thank you.

Last edited: May 2, 2015
2. May 3, 2015

### blue_leaf77

That's a classical, non (fully) quantum view.
In the present of perturbation such as external field, the true wavefunction of the electron can be represented as a linear combination of the unperturbed Hamiltonian eigenfunctions. So the expectation value of some observables such as radius is indeed time-dependent, but to say whether it either stays definitely in its orbital or change to another one is actually violating the QM postulate. As said above that the electron state can be expanded into superposition of the orbitals' wavefunction means that it has less-than-unity probability of ending up in various orbitals. In fact the lifetime of a given orbital is defined as the sum of all transition rates from that orbital toward the other possible orbitals
Is there any way an electron can change orbital with different energies without giving up its energy into some other form?
I'm not sure that there has been research which studies such transient behavior. You may want to look on this matter up yourself. Otherwise, to study this with sufficient accuracy, one should probably calculate the perturbed state up to some higher perturbation order.

Last edited: May 3, 2015