228
DOC.
38
QUANTUM
THEORY OF RADIATION
{2}
p'(v',*')-
p(v)^A(i
-2i
cos
Q).
(14')
Furthermore,
the
theory
of
relativity provides,
with the desired
approximation,
the
formulas
v
=
v'(1
-
v-c
cos
Q)
(15)
COS
(f)' =
COS
4
- v-c
+
v/c
cos2$
(16)
W'
=
W.
From
(15)
follows,
with
corresponding approximation,
(17)
v
=
v'(1
+
v-c
cos Q').
[p.
57]
Therefore,
and
likewise in the
desired
approximation,
p(v)
=
p(v'
+
v-cv'
cos Q')
or
P(v)
=
p(v')
+
4*V)
•
-v'
cos
4'.
dv
c
According
to
(15), (16),
and
(17)
there is
in
addition
dv
dv'
dK
=
1 +
-
COS
(f)'
c
sin
dd4dili
dK'
sin
cf)'
cty'dx|r'
d
(cos
f)
_
j
d
(cos
f')
2
-cos
f'
c
Due
to
these
two
relations and
(18), (14')
becomes
P'(v',*')
=
(p)v. +
-
v
cos
c
dv
/v'
(1
-
3
cos
t')
c
(18)
(19)
With the
help
of
(19)
and
our hypotheses on
the
spontaneous
emission and the
induced
processes
of the
molecule,
we can easily
calculate the
mean
value
of
momentum
per
time unit which
is
transferred to the molecule.
However,
before
we
do this
we
have to
say something
to
justify
the method used. One
could
object
that
equations
(14), (15),
(16)
are
based
upon
Maxwell's
theory
of
the
electromagnetic
field,
a
theory
that is
incompatible
with
quantum theory.
But this
objection
touches
the form
more
than the
essence
of
the matter.
Because,
in whichever
way
the
theory