Unified View of Spontaneous Emission in Several Theories of Radiation

  • J. H. Eberly


Consider the model classical field theory described by the Lagrangian density ℒ(x,t):
$$ \mathcal{L}\left( {x,t} \right) = \psi *\left( {x,t} \right)\left\{ {i\hbar \frac{\partial } {{\partial t}} - \frac{1} {{2m}}\left[ {\frac{\hbar } {i}\nabla - \frac{e} {c}A\left( {x,t} \right)} \right] - V\left( x \right)} \right\}\psi \left( {x,t} \right) + \frac{1} {{8\pi }}\left\{ {\left[ {\frac{1} {c}\dot A\left( {x,t} \right)} \right]^2 - \left[ {\nabla \times A\left( {x,t} \right)} \right]^2 } \right\}$$
Evidently, ℒ(x) is the beginning of a theory of the interaction of the fields ψ and A. There are several free parameters in the theory: ℏ, m, e, c.


Frequency Shift Spontaneous Emission Conjugate Momentum Unify View Interpretive Framework 
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References and Notes

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    By classical we mean that none of the interpretive framework of quantum field theory is involved, and that the dynamical fields are simple mathematical functions that commute everywhere and at all times with each other. Another discussion of possible consequences of (I) and (4) has been given by J. H. Eberly, in Laser Photochemistry, Tunable Lasers, and Other Topics,Eds. S. F. Jacobs et al.,Addison-Wesley, Reading, Massachussetts (1976), p. 421.Google Scholar
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    E. T. Jaynes, in Quantum Electronics,Ed. C. H. Townes, Columbia University Press, New York (1960), p. 288. The Hamiltonian form of our field theory has close parallels with this earlier development.Google Scholar
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Copyright information

© Springer Science+Business Media New York 1980

Authors and Affiliations

  • J. H. Eberly
    • 1
  1. 1.Department of Physics and AstronomyUniversity of RochesterRochesterUSA

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