Spectral lines and QM

Question

In the various presentations I've seen so far in atomic physics of series such as the Balmer series, the wavelength of each spectral line is definite - but in QM, free particles have no definite energy if I understand correctly: none of the photons in a beam of photons that would interact with the electron of an hydrogen atom would carry an energy corresponding exactly to a wavelength of 656.3 nm for example (I'm saying "none of the photons" because if we have a distribution of energies for the photons in the beam, in the limit, there is no particle at a single discrete value of energy). What happens exactly? Should Heisenberg uncertainty be taken into account? Is there a quantum mechanical account of photon absorption by atoms?

Answer 1

Of course the photon will have an amount of energy and that is radiation energy which if defined by Planck's equation. Radiation energy is also related directly to wavelength,frequency and wavelength number.The higher the energy, the less is the wavelength ( all this from Planck's equation). What Heisenberg equation is about, does not include the energy.It includes only the position and the rate of electrons ( you can't know both of them at the same time ). The absorbtion of radiaton by atoms is very well defined by absorbance formula A=abc.I hope I understood the question correct.