Analysis using the Einstein's coefficients is applicable to the state in which the thermal equilibrium is not achieved. However, if this is applied to the thermal equilibrium, we can obtain relations between these coefficients.

Assume the detailed balance is achieved between
the spontaneous emission, the induced emission and the absorption as

where represents the statistical weight for the state n.

Equation (2.144) gives

(2.146) |

Using equations (2.145) and (2.147), equation (2.144) reduces to

(2.148) |

(2.149) |

Kohji Tomisaka 2009-12-10