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Exploring Spontaneous Decay in QM with Griffiths
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[QUOTE="vanhees71, post: 6007621, member: 260864"] It is really important to get the idea about what a photon is straight from the very beginning. Usually atomic physics in the introductory textbooks is treated in the semiclassical approximation (in the terminology of quantum optics), i.e., the electrons in the atom are quantized (moving in a static (Coulomb) field, describing the much heavier nucleus), while light (electromagnetic waves) are treated classically. From this you only get absorption and induced emission. If you also want spontaneous emission you also have to treat the ligth (em. fields) as a quantum system, and only then you can talk about photons, which are special states of (free) electromagnetic fields, the socalled one-particle Fock states. Einstein has found the necessity for spontaneous emission before relativistic QFT and QED has been worked out completely, which happened in 1926 in the famous "Dreimännerarbeit", where Jordan already introduced the complete picture with the quantized em. field, but at this time most physicists considered this to go too far. So Jordan's contribution got forgotten, and usually Dirac is mentioned as the inventor of the quantized radiation field, where he explained spontaneous emission in a consistent way for the first time. Indeed, spontaneous emission is the most simple proof for the necessity of field quantization and thus, in the case of the em. field, photons. The claims in many introductory textbooks that the photoelectric effect or Compton scattering prove the existence of photons are flawed, because in modern QT the photoelectric effect at the level of Einstein's famous 1905 paper is easily derived in the semiclassical approximation (electrons quantized, em. field classical) using 1st-order time-dependent perturbation theory. No photons in sight, only classical electromagnetic fields! The same holds true for Compton scattering which has been derived by Klein and Nishina also in the semiclassical approximation first. In modern QED with the em field quantized you get this result in leading order perturbation theory by evaluating the tree-level Feynman diagrams, i.e., diagrams without closed loops. The closed loops provide the quantum effects of field quantization. Einstein's ingenious discovery of the necessity of spontaneous emission came from re-analyzing the problem of black-body radiation in terms of kinetic theory, considering the emission and absorption process of "photons" (in the "particle sense" of old quantum theory, which is completely wrong from the modern point of view of modern Q(F)T) at the walls of the cavity. To obtain the correct Planck law for the spectrum you have to take into account not only absorption and induced emission (which both is possible in the semiclassical approximation, i.e., with classical em. fields) but also spontaneous emission (which is possible only due to the quantum fluctuations of the electromagnetic field, i.e., from a modern point of view via its quantization). As I said, the final breakthrough to explain spontaneous emission came from Dirac's 1927 paper, introducing annihilation and creation operators for photons. [/QUOTE]
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