Hello!(adsbygoogle = window.adsbygoogle || []).push({});

My textbook quotes the probability W of a transition between the levels 1 and 2 of a laser that appears in the rate equations. For

[tex]E_2 = E_1 +h\nu[/tex]

it is supposed to be given by:

[tex]W = \frac{1}{\tau VD(\nu)\Delta\nu}[/tex]

where [tex] \tau [/tex] is the lifetime of the level 2 (probably for the case of spontaneous emission making the only important contribution), [tex] D(\nu)d\nu[/tex] is the number of modes of the field in the intervall [tex] (\nu,\nu+d\nu) [/tex] per unit volume of the laser substance and [tex] \Delta\nu [/tex] is the broadness of the spectral line corresponding to transitions between states 2 and 1.

There are no comments on how to prove this. I would appreciate help, since many important conclusions are driven from that formula.

I have also discovered the attached document, which derives a more complex formula:

[tex]W = g(\nu) \frac{A_{21}c^{2}I(\nu)}{8\pi h {\nu}^3}[/tex]

containing the Einstein coefficient for spontaneous emission, the radiation Intensity [tex] I(\nu) [/tex] and the line shape [tex] g(\nu) [/tex]. The formulas are fairly similiar if we remember the equalities:

[tex] A_{21} = \frac{1}{\tau} [/tex]

and

[tex] D(\nu) = \frac{8\pi{\nu}^2}{c^3} [/tex]

It would be sufficient if you could explain how to go from the second expression for W to the first one. It is the [tex] \Delta\nu [/tex] in particular that I do not see how to obtain!

Thanks for any help,

Angelos

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Transition Probability for a Laser system

Loading...

Similar Threads for Transition Probability Laser |
---|

I Use the Dirac Equation to calculate transition frequencies in Hydrogen |

I Rotational transitions |

B Does gravity affect quantum transition amplitudes? |

A Quantum Optics - transition from pure to mixed state |

**Physics Forums - The Fusion of Science and Community**