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.