DOC. 38
QUANTUM
THEORY OF RADIATION 223
a) "Ausstrahlung"
(Spontaneous Emission).
An
oscillating
Planck resonator
[9]
radiates
energy
in
a
known
manner according
to
Hertz, independent
of
whether it is
excited
by an
external field
of
not.
Correspondingly, a
molecule shall be able to
change
from state
Zm
into state
Zn
under emission
of
the
energy
em
-
en
with
frequency v
without external
causes.
The
probability
dW that this
actually occurs
during
the time element
dt
shall be
dW
=
Anmdt,
(A)
where
Anm
is
a
constant characteristic
of
the index combination under consideration.
[p. 51]
The assumed statistical law
corresponds
to
a
radioactive
reaction,
and the
assumed
elementary process
to
a
reaction where
only y-radiation
is emitted. One does
not need to
assume
that this
process requires no
time;
the time need
only
be
negligible compared
to the times
during
which the molecule is in states
Z1,
etc.
b) "Einstrahlung" (Induced Radiation).
In
a
field
of
radiation, a
Planck resonator
changes
its
energy
because the
electromagnetic
field
of
the radiation transfers work
upon
the resonator.
Depending upon
the
phases
of
the resonator and the
oscillating
field,
this amount
of
work
can
be
positive or negative.
In
taking
account
of
this,
we
introduce the
following
quantum-theoretic
hypotheses.
Under the action of the
[10]
radiation
density p
of
frequency v,
the molecule
can go
from state
Zn
to
Zm
by
absorbing
the radiation
energy
em
-
en
according
to the
probability
law
dW
=
Bnmpdt. (B)
In
a
similar
manner
the transition
Zm
-
Zn
is
possible
under the action of
radiation, whereby
the radiation
energy
em -
en
is set free
according
to the
probability
law
dW
=
Bnmpdt.
(B')
Bmn
and
Bnm
are
constants. Both
processes
are
called
"changes
of
state
by
'Einstrahlung' (induced radiation)."
The
question
is
now
what
momentum
is transferred
upon
the molecule
during
these
changes
of
state.
We
begin
with the induced
processes.
If
a
beam
of
radiation
with
a
certain direction does work
upon a
Planck
resonator,
the beam loses the
corresponding energy. According
to the momentum
theorem,
this transfer
of
energy
corresponds
to
a
transfer
of
momentum from the beam to the resonator. The latter
suffers the action
of
a
force
in
the direction
of
the
ray
of the beam.
If
the transfer
of
energy
is
negative,
the action
of
the force
upon
the resonator is also in the
opposite
direction. In
case
of
the
quantum hypothesis
it
obviously means
the
following.
If
the
[p.
52]
process
Zn
-
Zm
takes
place
due to induced
radiation,
then the molecule receives