DOC. 38
QUANTUM
THEORY OF RADIATION 229
of
electromagnetic processes may develop,
it will
certainly
retain
Doppler's principle
and the law
of
aberration,
and with it also
equations
(15)
and
(16). Furthermore,
the
validity
of the
energy
relation
(14)
extends
beyond
that
of
the
theory
of
undulation;
according
to
the
theory
of
relativity,
the
transformation law
applies,
for
example,
also
to
the
energy
density
of
a mass
that
moves
with the
(quasi)
speed
of
light
and is of
infinitesimally
small
density
when
seen
at
rest.
Equation
(19) can
therefore claim
validity
for
any theory
of radiation.-
[18]
The radiation in the solid
angle
dk'
would,
according
to
(B),
give
rise
to
Bmn
p(V',o')dk'/4n
induced
elementary processes per
second of
type
Zn
-
Zm
if the molecule
would
immediately
be
brought
back into
state
Zn
after each such
elementary process.
In
reality,
however,
it remains in
state
Zn
according
to
(5)-for
a
time
per
second
of
[p. 58]
1
=
Kt
sp"e
'
where
we
used the abbreviation
-
^n
-
g|TI
^
"
kT *
=
Pne
KI
+Pme
•
(20)
The number of
processes
is therefore in actual fact
Sn
1
- _
_
c/ic'
5p~e
ICBTmPCVI4/)
During
each
one
of these
elementary
processes
the momentum
Em-En/C
cos
O
is
transferred
to
the
atom
in the direction
of
the
positive
X'-axis. In
an
analogous
manner
we
found-based
upon
(B')-that
the
corresponding
number of induced
elementary processes
of
type
Zm
- Zn
per
second is
-
dk'/4n
and in this
case
the
momentum
-
Em-En
cos
o'
is transferred to the molecule with
each such
elementary process. Considering (6)
and
(9),
the total
momentum
per
time
unit that
is
transferred to the molecule and caused
through
induced
processes per
time
unit is