Hilborn has compared various formulations for derivations for the Einstein coefficients, by various authors.
2.
These things are important for the study of the Einstein coefficients, which relies partly on the notion of thermodynamic equilibrium.
3.
Combining the above two equations with the requirement that they be valid at any temperature yields two relationships between the Einstein coefficients:
4.
Where B _ { 12 } and B _ { 21 } are the Einstein coefficients for photo absorption and induced emission respectively.
5.
For the case of the presence of matter, quantum mechanics provides a good account, as found below in the section headed Einstein coefficients.
6.
The relationships between the Einstein coefficients will yield the expression of Kirchhoff's law expressed in the " Radiative transfer " section above, namely that
7.
The three parameters, and, known as the Einstein coefficients, are associated with the photon frequency produced by the transition between two energy levels ( states ).
8.
Where A _ { 21 } is the Einstein coefficient for spontaneous emission, which is fixed by the intrinsic properties of the relevant atom for the two relevant energy levels.
9.
The transition frequencies and the Einstein coefficients of transitions are well known and listed in various tables as in Boltzmann's formula might be used, the density dependence usually requires atomic modeling.
10.
For the case of isotropic absorption and emission, the emission coefficient ( ) and absorption coefficient ( ) defined in the radiative transfer section above, can be expressed in terms of the Einstein coefficients.
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