D O C U M E N T 1 4 2 N O V E M B E R 1 9 2 3 1 3 7
These processes, moreover, remove a peculiar difficulty. According to the out-
come of my calculations, it seems as if for given probability functions of the ele-
mentary processes, other radiation fields besides the Planck radiation field could
also remain in statistical equilibrium with the electron gas with a Maxwell velocity
distribution. Namely, all those for which holds.
Hence ; (1)
for Planck’s radiation law in particular a = 1. A corresponding situation applies in
the classical theory as well.
Rayleigh’s radiation law, is in fact not the general integral of the
differential equation
for ρν, which in the paper by you and Hopf resulted as a condition of thermal
equilibrium[3] (in the case of a free electron, the same differential equation fol-
lows.) This general integral rather reads
,
wherein A is an integration constant and results precisely out of (1) when the limit
for long waves is approached (i.e., ) after one sets a = 1 + Ah. The suspicion
suggested itself that this result was only apparent, faked by the approximation
method used. This is indeed the case now. Because, for your new elementary pro-
cesses of higher order, the condition for thermal equilibrium of the general radia-
tion field (1) for any a is only satisfied when the number of emitted quanta is spe-
cifically the same as that of the absorbed quanta for the elementary process being
examined. Generally this does not, by any means, need to be valid, and then a = 1
necessarily follows, as is easily seen. The Planck radiation field is therefore the
only one in which the condition for thermal equilibrium is satisfied for all kinds of
elementary processes at the same time. One may well suspect that the same will
analogously hold also for the calculation on the basis of the classical theory.
Now another final remark. You write that the probability of an elementary act,
in which the quanta are absorbed and the quanta are
αν3
ρν
--------- +
©
§ ·
e

kT
–------
konst. a = =
ρν
αν3
aekT

------
1
------------------- -= α
8πh
c3
---------·
-=
© ¹
§
ρν
8πν2
c3
------------kT =
c3
48πν2
---------------ρν 2
1
2
--kT§
- ρν
ν∂ρν·
3
-- -
ν∂

© ¹
0 =
ρν
8πν3
c3
----------------------------
1
ν
kT
----- - A +
=
h 0
hν1…hνp hνp
1 +
…hνp
q +
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