- #1
Jano L.
Gold Member
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If I may, I would like to give this question another try, especially if guys with some cabala in QFT can address it.
Is it possible to show in the relativistic quantum theory, that the hydrogen atom is stable? (Electron will not fall onto the proton)?
I explain.
In the non-relativistic quantum theory the system is described by an Hamiltonian derived from the classical Hamilton's function for Kepler's problem [itex]H = \frac{p^2}{2m} - \frac{Ke^2}{r}[/itex].
But this immediately implies the system is conservative. There is no radiation, no spontaneous emission in the model. No surprise that both in classical and quantum theory the hydrogen atom is stable.
But such an Hamiltonian is correct only in a non-relativistic theory (if the Galilei invariance of laws was accepted). In the relativistic theory, the retardation of the EM field and thus of radiation should be taken into account. I suspect that this is not possible to do within the standard Hamiltonian.
The outgoing radiation can however draw energy away if the particles accelerate and the relativistic quantum model of hydrogen atom can still be unstable for the same reason as in the classical model of the hydrogen atom which takes into account the radiation: the accelerated particles will radiate and lose energy.
What do you think? Is there a way in QFT to describe the hydrogen atom exactly (at least in principle) and show it has a stable ground state?
Is it possible to show in the relativistic quantum theory, that the hydrogen atom is stable? (Electron will not fall onto the proton)?
I explain.
In the non-relativistic quantum theory the system is described by an Hamiltonian derived from the classical Hamilton's function for Kepler's problem [itex]H = \frac{p^2}{2m} - \frac{Ke^2}{r}[/itex].
But this immediately implies the system is conservative. There is no radiation, no spontaneous emission in the model. No surprise that both in classical and quantum theory the hydrogen atom is stable.
But such an Hamiltonian is correct only in a non-relativistic theory (if the Galilei invariance of laws was accepted). In the relativistic theory, the retardation of the EM field and thus of radiation should be taken into account. I suspect that this is not possible to do within the standard Hamiltonian.
The outgoing radiation can however draw energy away if the particles accelerate and the relativistic quantum model of hydrogen atom can still be unstable for the same reason as in the classical model of the hydrogen atom which takes into account the radiation: the accelerated particles will radiate and lose energy.
What do you think? Is there a way in QFT to describe the hydrogen atom exactly (at least in principle) and show it has a stable ground state?