I would like to calculate the intensities of Hydrogen spectral lines for the case of Hydrogene at temperature T contained inside a volume V. I reckon that what I need is 1)The mean population of the upper energy level 2)The probability of transition between the levels I believe that the mean population of a quantum state will be given by Bose statistics, so that of an energy level will be the same multiplied by the degeneracy of the energy level. For the transition probabilities I have no clue. When we deal with atoms subjected to a field those are usually calculated by perturbation theory, for which one needs a perturbative Hamiltonian. I have no clue how to arrive at the latter here. Nor do I think that the influence of the whole surrounding would be small enough to be a perturbation. Help is really appreciated!