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arXiv:1502.06404 · Physics Letters A

Spontaneous light emission by atomic hydrogen: Fermi's golden rule without cheating

Vincent Debierre, Thomas Durt, André Nicolet, Frédéric Zolla

Published Jun 12, 2015• 8 citations
arXivHTMLPDF
DOI
10.1016/j.physleta.2015.06.011

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Equivalent derivations of time-dependent pertubation theory; Fermi golden rule; the Born approximation for scattering from Fermi golden rule; survival probability of a state in a time-independent perturbation; positronium in static and oscillating magnetic fields; hydrogen atom in a time-dependent electric field; a model for inelastic scattering of a projectile with a target; semiclassical treatment of the electromagnetic field; ionization of the hydrogen atom by an electromagnetic wave; cross sections for stimulated absorption and emission in hydrogen; spontaneous emission and selection rules with an application to the 2p to 1s transition in hydrogen; theory of the line width; formal scattering theory; S- and T-operators.
In the present work we have worked out a vector model for spontaneous emission based on the principle of moving vectors.This simplified approach reflects the work of Weisskopf and Wigner.Normalized probability of a transition to an upper level versus detuning has been plotted.Further we have shown that the areas which have been generated at phasor diagrams in different values of decay constants for moving vectors are directly proportional to time.This is a manifestation of Fermi's Golden rule.Fermi's Golden Rule in quantum mechanics is well known.But it is for the first time that we have worked out the concept of moving vectors using the transition probabilities and the concept of phasor diagrams to represent the Fermi's Golden rule.