The role of Max Born in the creation of the quantum theory is discussed. Some explanations as to why he received his Nobel Prize so late are offered.

1.
Some of the more notable biographies include the following:
Albrecht
Fölsing
,
Albert Einstein
(
Penguin Books
, New York,
1998
);
Abraham
Pais
,
Niels Bohr’s Times
(
Oxford University Press
, New York,
1991
);
Walter J.
Moore
,
Schrödinger, Life and Thought
(
Cambridge University Press
, New York,
1992
);
Abraham
Pais
,
Maurice
Jacob
,
David I.
Olive
, and
Michael F.
Atiyah
,
Paul Dirac: The Man and His Work
(
Cambridge University Press
, New York,
2005
);
David C.
Cassidy
,
Uncertainty; The Life and Science of Werner Heisenberg
(
W. H. Freeman and Co.
, New York,
1992
).
2.
The play in question is
Michael
Frayn
,
Copenhagen
(
Anchor Books
, New York,
2001
).
3.
Nancy Thorndike
Greenspan
,
The End of a Certain World
(
Basic Books
, New York,
2005
).
4.
Reference 1, p.
144
.
5.
Reference 1, p.
2
.
6.
Barbara
Goldsmith
,
Obsessive Genius: The Inner World of Marie Curie
(
Atlas Books
, W. W. Norton & Company, New York,
2005
).
7.

Goldsmith does not seem to understand that krypton was also produced in the fission whose mass Meitner had to know.

8.
Reference 4, p.
225
.
9.
Reference 1, p.
62
.
10.
For a wonderful view of Göttingen see John Derbyshire,
Prime Obsession
(
Joseph Henry Press
, Washington, DC,
2003
). In contrast to the two books I have mentioned, Derbyshire’s book, which concerns Riemann’s hypothesis about the zeros of the Riemann function, is a model of how a popular science book should be written.
11.
This quote is from
Constance
Reid
,
Hilbert
(
Springer
, New York,
1996
).
12.
The Born-Einstein Letters: Friendship, Politics and Physics in Uncertain Times
, with an introduction by Kip Thorne and Diana Buchwald (
McMillan
, New York,
2005
).
13.
Reference 1, p.
61
. The italics are mine.
14.
A.
Einstein
, “
Strahlungs-Emission und -Absorption nach der Quantentheorie
,”
Verh. Dtsch. Phys. Ges.
18
,
318
(
1916
).
15.
A good account can be found in
David
Bohm
,
Quantum Theory
(
Dover
, New York,
1989
). Bohm compares the answer found in this way with the real quantum mechanical answer and shows that at least in simple cases they agree surprisingly well.
16.
A account of this chronology can be found in
David
Cassidy
,
Uncertainty; The Life and Science of Werner Heisenberg
(
W. H. Freeman
, New York,
1992
).
17.
I have been greatly helped by two papers that I would suggest reading in the following order. First,
William A.
Fedak
and
Jeffery J.
Prentis
, “
Quantum jumps and classical harmonics
,”
Am. J. Phys.
70
(
3
),
332
344
(
2002
);
and
Ian J. R.
Aitchison
,
David A.
MacManus
and
Thomas M.
Snyder
, “
Understanding Heisenberg’s ‘magical’ paper of July 1925: A new look at the calculational details
,”
Am. J. Phys.
72
(
11
),
1370
1379
(
2004
);
A translation of the original paper can be found in
Sources of Quantum Mechanics
, edited by
B. L.
van der Waerden
(
Dover
, New York,
1967
), pp.
261
276
.
18.
See
van der Waerden
, Ref. 13, p.
261
.
19.

Here and in what follows I will ignore the following subtlety. In general these transition amplitudes are complex numbers and the squares are absolute values squared. For purpose of this review I will treat them as if they were real numbers. This will not affect anything.

20.
Reference 1, p.
125
.
21.
See
van der Waerden
, Ref. 13, p.
266
.
22.
For a discussion see
Marshall
Bowen
, and
James
Coster
, “
Born’s discovery of the quantum-mechanical matrix calculus
,”
Am. J. Phys.
48
(
6
),
491
492
(
1980
).
23.
These are clearly spelled out in Aitchison et al., Ref. 13, Appendix A.
24.

The time dependence of xnm(t) is eiωnmt. The velocity is the first time derivative hence the factor of i, while the acceleration is the second time derivative so you get i2.

25.
See
van der Waerden
, Ref. 13, p.
40
.
26.

Most of it is reproduced in translation in van der Waerden, Ref. 13. For reasons that are unclear van der Waerden leaves out the last few pages of the original which Jordan later complained about.

27.
Van der Waerden
, Ref. 13, p.
277
.
28.

I am grateful to Helmut Rechenberg for remarks on Jordan’s career and other points in my review.

29.
This full text of this and many other wartime pronouncements of German scientists can be found in
Physics and National Socialism
, edited by
Klaus
Hentschel
(
Birkhäuser
, Boston,
1996
), p.
272
.
30.

I am grateful to Peter Goddard for supplying this and for his comments.

31.
Later in 1926, Dirac published a second paper in which he used matrix methods to discuss the hydrogen atom. See
P. A. M.
Dirac
, “
Quantum mechanics and a preliminary investigation of the hydrogen atom
,”
Proc. R. Soc. London, Ser. A
110
,
561
(
1926
)]. In this paper he does refer to Born and Jordan.
32.
Reference 1, p.
191
.
33.
M.
Born
, “
Zur Quantenmechanik der Stoßvorgänge
,”
Z. Phys.
37
,
863
867
(
1926
);
Quantenmechanik der Stoßvorgänge
,”
Z. Phys.
38
,
803
827
(
1926
).
34.

One again I am ignoring the fact that these functions are in general complex numbers so that you must take the absolute value squared.

35.
This quotation can be found in
Abraham
Pais
,
Subtle is the Lord
(
Oxford University Press
, New York,
1982
), p.
442
. The first bracket is mine and the other two are Pais’s.
36.
Reference 30, p.
443
.
37.
See
M.
Born
, “
The statistical interpretation of quantum mechanics
,” in
Nobel Lectures in Physics 1942–1962
(
Elsevier
, Amsterdam,
1964
).
38.
Reference 1, p.
159
.
39.
M.
Born
and
L.
Infeld
, “
Foundations of the new field theory
,”
Proc. R. Soc. London, Ser. A
144
,
425
451
(
1934
).
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