222 DOC. 38
QUANTUM
THEORY OF RADIATION
following
considerations.
§1.
The Fundamental
Hypothesis
of
Quantum
Theory.
Canonical Distribution of States
According
to
quantum theory,
a
molecule
of
a
distinct
kind can-aside
from
orientation and
translatory
movement-take
only
a
discrete
sequence
of
states
Z1,
Z2,...,Zn,...
with
(inner) energies
e1,
e2,...,en,....
If
these molecules
are
part
of
a
gas
of
temperature
T,
then the relative
occurrence
Wn
of
these states
Zn
is
given
by
the canonical
partition
of
states
of
statistical mechanics
according
to the
formula,
wn
=
P.'~*
•
(5)
In this formula k
=
R/N
is
the well-known Boltzmann
constant;
pn can
be called the
[p.
50]
statistical
"weight"
of
the
state and is
a
number characteristic
of
the molecule,
namely
its n-th
quantum
state,
and
it is
independent
of
T.
Formula
(5) can
be derived from
Boltzmann's
principle or
in
a
purely thermodynamic manner. Equation (5) expresses
the
farthest-reaching generalization
of
Maxwell's law
of
velocity
distribution.
The
most recent
principal
advances
of
quantum theory
deal with the theoretical
determination
of
quantum theoretically possible
states
Zn
and their
weights
pn.
For
our present principal investigation
a
closer determination
of
these
quantum
states is
not
required.
§2.
Hypotheses Concerning
the
Energy Exchange by
Radiation
Let
Zn
and
Zm
be two
quantum theoretically possible
states
of
a
gas
molecule,
and
their
respective energies
en
and
em
shall
satisfy
the
inequality
em en.
The molecule shall be able to
change
from state
Zn
into state
Zm
under
absorption
of the radiation
energy
em
-
en;
likewise,
a
change
from state
Zm
into state
Zn
shall
be
possible
under emission
of
radiation
energy.
The radiation absorbed
or
emitted
by
the molecule shall be
of
frequency
v,
which is characteristic
of
the
index combination
(m,n).
For the laws that
determine this
transition
we
introduce
several
hypotheses
that
are
obtained from the known
circumstances of the classical
theory
of
Planck's
resonator,
and transferred to the still unknown
ones
of
quantum
theory.