Abstract
SYNGE1 has discussed a relativistic extension of the Bohr formula, hv′=E′−E, for the frequency of the emitted light quantum between two levels of a quantum system:where m′ and m are the total masses of the two states. Equation (1) is a simple consequence of the covariant energy-momentum conservation at the vertex m′→m+y, evaluated in the rest frame of the state with mass m′. In the rest frame of m, we have instead of (1), hv=(m′2−m2)/2mc. It is also clear that equation (1) can be written formally as hv′ = E′ − E, in the rest frame of m′2, because E′ = m′ in the rest frame of m′, and because the correct equation is hv′ = m′−E, all quantities in the rest frame of m′. If the emitted quantum is not the light quantum but any system (or system of particles) with the total invariant mass μ we obtain, again by the energy-momentum conservation at the vertex m′−m+μ, instead of (1),where hv′ is the total relativistic energy of the emitted quantum.
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References
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BARUT, A. Relativistic Bohr Formula. Nature Physical Science 230, 180 (1971). https://doi.org/10.1038/physci230180a0
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DOI: https://doi.org/10.1038/physci230180a0