Planck's Derivation of Transition Probabilities and Einstein's Quantum Theory of Radiation

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  • Planckの遷移確率の導出とEinsteinの輻射の量子論
  • Planck ノ センイ カクリツ ノ ドウシュツ ト Einstein ノ フクシャ ノ リョウシロン

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Abstract

In 1916 Einstein considered a thermal equilibrium between blackbody radiation and gas molecules in a cavity. On this occasion he introduced probability coefficients A and B of spontaneous and induced transitions, respectively. Then, he derived the ratio A/B (Eq. (4) in the text). With respect to this, Planck, in the fourth edition of his book (1921), Lectures on the Heat Radiation, derived the individual equation of A (Eq. (13)). Furthermore, it is quite interesting that in the course of derivation Planck introduced the substitution of a difference quotient (Eq. (11)) for a differential one (Eq. (9)). Thus, it should be noted that Planck employed this mathematical manipulation earlier than Kramers. This paper also argues that Planck's idea of difference quotient stems from the energy fluctuation based on the Fokker equation (7).

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