220
DOC.
38
QUANTUM
THEORY OF RADIATION
Doc.
38
On the
Quantum
Theory
of Radiation
by
A. Einstein
[p.
47]
[1]
The formal
similarity
between the
curve
of
the chromatic
distribution
of thermal
radiation and the Maxwellian distribution law of velocities is
so
striking
that it could
not
have been hidden for
long.
As
a
matter
of
fact,
W. Wien
was already
led
by
this
[2]
similarity
to
a
farther-reaching
determination
of
his radiation formula in his
theoretically important paper,
where he derives his
displacement
law
P
=
v3f(v/T).
(1)
As is well
known,
he found in this
pursuit
the formula
-h\
p
=
av3e kT,
(2)
which is still
recognized today as a limiting
law for
large
values
of
v/T
(Wien's
[3]
[4]
radiation
formula).
We know
today
that
an analysis
that is based
upon
classical
[5]
mechanics and
electrodynamics
cannot
provide a
usable radiation
formula;
the
classical
theory
leads
instead, by necessity,
to
Rayleigh's
formula
p
=
*EV27\
(3)
When
Planck,
in his
fundamental
investigation,
based his radiation
formula
p
=
av3-
(4)
h\
kT
-1
upon
the
postulate
of
discrete elements
of
energy (upon
which
quantum theory
[6] developed
in
quick
succession),
Wien's
investigation-which
had
led
to
equation
(2)-was,
naturally,
quickly
forgotten.
Recently
I
was
able
to
find
a
derivation
of
Planck's radiation
formula1
which I
based
upon
the fundamental
postulate
of
quantum
theory,
and which
is
also related
[p.
48]
to the
original
considerations
of
Wien such that the relation between Maxwell's
curve
and the chromatic distribution
curve comes
to the fore. This derivation deserves
attention
not
only
because
of
its
simplicity,
but
especially
because it
seems
to
clarify
[7] 1
Verh. d.
deutschen
physikal. Gesellschaft
13/14 (1916),
p.
318.
The
considerations in
the
quoted paper
are repeated
in
the
present investigation.