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Planck's constant $\hbar$ is the scale of quantum mechanics' contributions to all quantities with the units of action – e.g. the action itself, angular momentum, product of position and momentum, the ratio of energy and frequency, and so on. Quantum mechanics dictates rules that specify not only the "order of magnitude estimate" but the precise values of ...


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I think both the link and the question refer to Dyson's heuristical argument on why the perturbative series in QED could not be convergent. It goes somewhat like this: Suppose the series in $\alpha$ converges in some radius. The it converges also for negative values of the coupling constant inside that radius. Consider now what kind of theory is QED with a ...


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While the answers above already answered your question, I would like to recommend a paper by myself: Nonsmooth and level-resolved dynamics illustrated with a periodically driven tight binding model. In this paper, we derived Fermi golden rule as a by-product. Our derivation does not use the delta function. I believe our derivation is much simpler and ...


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The WKB approximation can be derived using an expansion in powers of $\hbar$. However, that doesn't imply that it can only be used if some quantum number is big. For example, a classic application of the WKB approximation is to alpha decay, which typically occurs from the ground state.


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No it doesn't mean higher values of m, as m here represents the set of orthonormal eigenstates of the system under study. In order to better understand where and how one arrives at 1st, 2nd, 3rd, ... order corrections, you need to look at the derivation of time independent perturbation theory that you find in most QM textbooks, there's also a rather detailed ...



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