- #1
itssilva
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As a rule of thumb, we might say that quantum theory becomes essential when we're analyzing systems at small distances (of the order of atomic sizes or less) and few enough particles (suppose particle number is conserved, as in QM); however, the world as a whole is quantum, and even a system which can succesfully be described by the classical framework is amenable to have its predicted values (energies, position expectation, etc) corrected to a small degree; such is also with electrodynamics.
However, I haven't been able to figure under which conditions you HAVE to consider the quantum nature of the EM field to have reasonable agreement with experiment, at the same level as in, we can't adequately describe electrons in atoms with classical mechanics. I know, for instance, of the existence of the Lamb shift, but overall it's a tiny correction to the relativistic energy eigenvalues of the hydrogen atom; are all quantum corrections of the EM field doomed to be small like it, or are there some conditions - particularly within atomic physics - under which they lead to results very distinct from the classical/semiclassical approach?
However, I haven't been able to figure under which conditions you HAVE to consider the quantum nature of the EM field to have reasonable agreement with experiment, at the same level as in, we can't adequately describe electrons in atoms with classical mechanics. I know, for instance, of the existence of the Lamb shift, but overall it's a tiny correction to the relativistic energy eigenvalues of the hydrogen atom; are all quantum corrections of the EM field doomed to be small like it, or are there some conditions - particularly within atomic physics - under which they lead to results very distinct from the classical/semiclassical approach?