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5

There are very strict limits on the mass of the photon already, so it would only affect our understanding of physics on the largest scales. The cosmologists would have some hard thinking to do, for instance. However, contrary to a comment, it would not affect relativity beyond requiring us to reconsider the usual name for $c$: not "the speed of light" but ...

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First your statement "In the photoelectric effect however the photon seems to give all it's momentum and energy to the electron" is not correct. In Photoelectric, the photon gives 'all' its energy to the electron, but most photon momentum goes to the more massive atom, the bind force between the electron and the atom serves as a transient of momentum. Due to ...

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You should be able to show by direct substitution that your proposed wave function $\tilde{\psi}(\mathbf{x},t)$ solves the Schroedinger equation, where the vector potential is included via the minimal coupling prescription $$\mathbf{p} \to \mathbf{p} - \mathrm{i} q \mathbf{A}(\mathbf{x})$$ (up to a sign convention for $\mathbf{A}$ and some dimensionful ...

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From right to left: outgoing electron $e^-$ spinor: $\bar{u}(p_2)$ QED vertex: $ie\gamma^\nu$ outgoing photon: $e^*(k_2)$ electron propagator: $\frac{i}{\not{q}-m+i0}$ incoming photon: $e(k_1)$ QED vertex: $ie\gamma^\mu$ incoming electron $e^-$ spinor: $u(p_1)$ There is no photon propagator in this process, and also, only one electron propagator. You ...

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In fact there is a difference, since the field per photon is stronger inside a cavity than in free space. The first treatment I know of is that of Jaynes and Cummings, Proceedings of the IEEE, Vol 51, p 89 (1963). This leads to an enhanced rate of spontaneous emission inside the cavity, called 'cavity enhancement', which is considered the cornerstone of ...

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The solution of the Schrodinger equation for the Hydrogen atom (and the Dirac equation yields the same solutions) is very successful in giving the Lyman series. It is a postulate that the difference in the energy levels leaves as a real photon, and gives the observed spectra. This is first quantization. When one talks of gauge invariance leading to ...

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