230 DOC.
38
QUANTUM
THEORY OF RADIATION
hv'/cs
pnBns
(e-
1+v/c)
+
(v'
Q')
cos
Q
[19]
where the
integration
is
to
be extended
over
all
solid
elementary angles. Executing
this
integration
and
using (19),
one
finds
-
hv/c2S
(p
-
1/3)pnBnm(e
1)
The effective
frequency
is here
again
denoted
by v
(instead
of
v').
This
expression represents, however,
the entire
momentum
which in
the
mean
is
transferred
per
time unit
to
a
molecule
moving
at
velocity
v.
It
is clear
that the
elementary processes
of
spontaneous
emission which
occur
without the interaction of
radiation
cannot
have
a preferential
direction
when
viewed from the
system
K', and
therefore in the
mean are
not
able
to
transfer
any
momentum to
the
molecule. The
end result of
our
deliberation
is
therefore
R
=
hv/c2S
(p
-
1/3)
PnBme
[p.
59]
(21)
§6.
Calculation of
A2
It is much
simpler
to
calculate the effect the
irregularities
of the
elementary process
have
upon
the
mechanical
behavior
of
the
molecule, because,
with the
degree
of
approximation we
considered sufficient from the
beginning,
one can
base the
calculations
upon
a
molecule at
rest.
Let
some
event
cause
the transfer
of
a
momentum
A
to
a
molecule
in the
X-
direction. In the various
cases
these
momenta
shall be of diverse
signs
and diverse
magnitudes.
Let
A
be
subject
to
a
law
of
statistics such that the
mean
value
of
A
vanishes. Now let
A1,
A2,...
be the values of the
momenta
of
several
mutually
independent
causes,
all
transferred
upon
the molecule and all
acting
in the X-direction
such that the
total
of
the
momenta
A
which
are
transferred is
given by
A
=
EAv.
If
the
mean
value
Av
for the individual
Av
vanishes,
one
has
A2 =
EA2v.
(22)
If
the
mean
values
Av2
of the individual
momenta
are
equal among
each other
(=A2)
and
l
is the
total number of
momenta-producing
causes,
one
gets
the relation
[20]