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I am aware this question has been asked before, but I am looking for a more technical answer than those given to the other questions.

I am aware the question in the title is a problem in classical mechanics that quantum mechanics solves. But it doesn't seem immediately obvious at first blush how QM accomplishes this. For the simple hydrogen atom case, you model the electron as experiencing a static potential and also coupled to the surrounding radiation field.

From this $H$ there will be certain stationary states (for the joint electron-field system), but it doesn't seem obvious that these stationary states will involve nice atomic orbitals. You could imagine that the vast majority of the stationary states involve almost all the energy being stored in the field, and so any initial state with the electron orbiting the atom will not be an eigenstate and so tend to dissipate its energy to the field over time.

Is there a "deep" reason why this isn't the case, or is it just something that comes out of the mathematics?-

John Rennie
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UtilityMaximiser
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  • Related: https://physics.stackexchange.com/q/20003/2451 and links therein. – Qmechanic Feb 02 '18 at 14:03
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    Possible duplicate of Why don't electrons crash into the nuclei they “orbit”? – John Rennie Feb 02 '18 at 14:33
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    In QM electron is atoms do normally radiate away all their energy. The point is that the lowest energy state is not a point particle sitting on the nucleus. – By Symmetry Feb 02 '18 at 14:33
  • It isn't clear to me what you are asking. Only the lowest energy state cannot radiate away its energy, because there is no lower state for it to decay to. So are you asking why there is a lowest energy state? – John Rennie Feb 02 '18 at 15:13
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    The issue I see with the answers to the "duplicate" question is that they appeal to the orbitals of the hydrogen atom. But this seems like question-begging since the coupling to the radiation field is not modelled in that model. So obviously it's not going to radiate away it's energy in such a model! Furthermore you can't argue that the hydrogen orbitals are stationary states and so stable, since the whole point is that they may no longer be stationary after a field coupling term has been added. – UtilityMaximiser Feb 02 '18 at 15:14
  • I suppose on further reflection, this is ultimately a question of why is the spectrum of the atom bounded from below. And the answer to that may be that the uncertainty principle forbids the electron from being localised arbitrarily close to the nucleus. – UtilityMaximiser Feb 02 '18 at 15:19
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    The uncertainty principle provides a rough and ready answer, but if I wanted to be very careful I would focus on the notion of what "acceleration" means to a quantum state leading to a rule like "charged particles radiate energy proportional the the second time derivative of their quantum states" and noting that orbitals are basically stationary state. – dmckee --- ex-moderator kitten Feb 02 '18 at 17:04
  • You ask "Why don't electrons in atoms radiate away their energy?". It is an observational fact that they do not, we would not exist if they did as atoms would not exist.So this is a basic observation, and the postulates of quantum mechanics which are in a sense extra axioms that pick up the relevant solutions of the differential equations ,( the simplest the Schrodinger with a potential), were decided upon so as to fit the hydrogen data, to start with, the spectral series fitted by Bohr. – anna v Feb 02 '18 at 18:12
  • Thus the answer is : because the qm postulates were picked so that the mathematics fits the observations, and is predictive of new systems. – anna v Feb 02 '18 at 18:12

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