1 2 6 D O C . 1 2 9 T H E O R Y O F R A D I A T I O N E Q U I L I B R I U M
apply instead of Planck’s at thermal equilibrium, and views this term as the quan-
tum theoretical expression for the properties of radiation that in the wave theory ap-
pear as interference variations.
One of us has indicated in an earlier
paper1)
statistical elementary laws for the
absorption and emission of radiation by a Bohr-like atom, from which Planck’s ra-
diation formula follows. We now set ourselves the task of connecting those earlier
posited elementary laws with formula (1) in such a way that the foundations for
both of the theoretical considerations be derived from a uniform and more general
point of view. It is, in fact, shown that a certain deepening of our understanding
about the interaction between radiation and material particles can be gained this
way. In the following exposition let us start out from the original elementary laws
and generalize them step by step.
§1. The Original Statistical Hypotheses and Their Relation to Planck’s Radia-
tion
Formula.2)
Let us consider a molecule or atom capable of certain quantum
states Z. Let Z and Z* be two such states with energy ε resp. ε* (ε* ε), which can
be converted into each other by absorption or emission of a quantum ε* ε = hν.
Let it be within an isotropic radiation field whose radiation density ρ is preliminari-
ly any function of ν. For the transitions between states Z and Z*, the following
probability rules will govern: 1. For the transition of one molecule in state Z into
Z* upon absorption of one quantum (positive induced radiation),
. (2)
2. For the transition of a molecule in state Z* into Z upon emission of one quantum
under the influence of the radiation field (negative induced radiation)
. (3)
3. For the transition of a molecule in state Z* into Z upon emission of one quantum
without any influence by the radiation field (spontaneous emission)
. (4)
The total probability for a transition Z* Z of a molecule in Z′ is hence
. (5)
The weights or probabilities of quantum states Z are thereby all assumed to be
equal (= 1). We assume that we can always conceive quantum states of higher
weight as incarnations of multiple different discrete quantum states of equal
energy.
If there are many such molecules in the radiation, then Boltzmann’s relation
1)
Einstein, Phys. Z[eit]s[chrift vol.] 18, [pp.] 121–128,
1917.[2]
2)
This section contains nothing new compared to the cited earlier treatise.
[p. 302]
dW bρdt =
dW bρdt =
dW′ adt =
dW a bρ)dt + ( =
[p. 303]
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