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

--------- 1¹ +

©

§ ·

e

hν

kT

–------

konst. a = =

ρν

αν3

aekT

hν

------

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 +