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Of course in the spectrum of QED there is hydrogen atom. The problem is what to compute in the case of bound states and how to compute. The usual approach to a general QFT is perturbative, meaning that you start from free fields (in this case electron and photon) and then you think the compulg coupling between these fields (in this case $\bar\psi ...


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The average separation of the electrons (integrated over time) in parahydrogen state is more than the average separation of the electrons in orthohydrogen state. And whenever electrons are away from each other, by nature, they would feel less Coulomb force and hence a lower energy state. This handwaving explanation can be justified in quantum mechanics more ...



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