212

DOC. 34 EMISSION

&

ABSORPTION OF RADIATION

Doc.

34

Emission and

Absorption

of Radiation in

Quantum Theory

by

A. Einstein

(Received

on

July

17, 1916)

[p.

318]

Sixteen

years ago,

when

Planck

created

quantum theory

by deriving

his radiation

[1]

formula,

he took the

following approach.

He calculated the

mean

energy

E of

a

resonator

as a

function of

temperature according

to

his

newly

found

quantum-

theoretic basic

principles,

and determined from this the radiation

density

p as a

function of

frequency v

and

temperature.

He

accomplished

this

by

deriving-based

upon electromagnetic

considerations-a

relation between radiation

density

and

[2]

resonator

energy

E:

E

=

-^£-.

(1)

87tv2

His derivation

was

of

unparalleled

boldness,

but found

brilliant confirmation. Not

only

the radiation formula

proper

and

the calculated

value

of

the

elementary quantum

[3]

in it

was

confirmed,

but

also

the

quantum-theoretically

calculated value

of

E

was

[4]

confirmed

by

later

investigations

on

specific

heat. In this

manner, equation (1),

originally

found

by electromagnetic

reasoning, was

also confirmed.

However,

it

remained

unsatisfactory

that the

electromagnetic-mechanical analysis,

which led

to

[5]

(1),

is

incompatible

with

quantum theory,

and

it is

not

surprising

that Planck

himself

and all theoreticians

who

work

on

this

topic incessantly

tried to

modify

the

theory

[6]

such

as

to

base it

on

noncontradictory

foundations.

[7]

Since

Bohr's

theory

of

spectra

has achieved its

great

successes,

it

seems

no

longer

doubtful

that the basic idea

of

quantum

theory

must be maintained. It

so

appears

that

the

uniformity

of

the

theory

must be established such that the

electromagneto-mechanical

considerations,

which led

Planck

to

equation (1), are

to

be

replaced by quantum-theoretical contemplations

on

the interaction between

matter

[p. 319]

and radiation.

In

this

endeavor I feel

galvanized by

the

following

consideration,

[8]

which

is

attractive both for its

simplicity

and

generality.

§1.

Planck's Resonator

in

a

Field

of Radiation

The behavior

of

a

monochromatic resonator in

a

field

of

radiation,

according

to the

classical

theory, can

be

easily

understood

if

one

recalls the

manner

of

treatment that

[9] was

first used in the

theory

of

BROWNian

movement. Let

E

be the

energy

of

the