DOC. 45 QUANTUM THEOREM

567

Published in Deutsche

Physikalische Gesellschaft. Verhandlungen

19

(1917):

82-92. Lecture

held

on 11

May 1917.

Published

30 May

1917.

[1]See

Sommerfeld

1914 and

Debye

1914

for discussions and

applications

of the

quantum

condition

for

systems

with

one

degree

of freedom. See also Mehra and

Rechenberg

1982,

chap.

II.4,

for

a

historical discussion of

quantum

conditions

in

early quantum theory.

[2]See

Sommerfeld

1915,

1916

for Arnold Sommerfeld's discussion of

systems

with several

degrees

of freedom.

[3]See

Epstein

1916a, 1916b,

and

Schwarzschild

1916c.

In

his

obituary

of Karl Schwarz-

schild,

Einstein 1916h

(Doc.

33),

Einstein calls the latter

paper

"a subtle

investigation"

("eine

feinsinnige Untersuchung").

[4]See, e.g., Appell

1904 (which is in

Einstein's

personal library)

or

Goldstein

1980

for dis-

cussions of Jacobi's theorem.

In

Einstein

1917f (Doc.

47)

Einstein

gives

a new

derivation

of

the theorem.

[5]"an"

should be

"al,"

and

"ßn"

in

the

following

line should

be "ßl."

[6]See

also Einstein

to

Paul

Ehrenfest,

3

June

1917,

for Einstein's

summary

of this

paper

and the discussion

in

the Introduction for

more

historical

background.

[7]See Gutzwiller 1990,

pp.

208-211,

for

a

modern

interpretation

of Einstein's

procedure

in

terms

of

invariant

tori

in

phase space

and of

the

relation between Einstein's

paper

and the the-

ory

of

classical chaotic

systems.