I give a pedagogical introduction to Bohm’s interpretation of quantum theory, suitable for graduate students.
REFERENCES
1.
J. S.
Bell
, Speakable and Unspeakable in Quantum Mechanics
, 2nd ed. (Cambridge U. P.
, Cambridge
, 2004
), p. 160
.2.
3.
4.
Murray
Gell-Mann
(private communication).5.
6.
L.
de Broglie
, Electrons et Photons: Rapports et Discussions du Cinquième Conseil de Physique tenu à Bruxelles du 24 au 29 Octobre 1927 sous les Auspices de l’Institut International de Physique Solvay
(Gauthier-Villars
, Paris
, 1928
).7.
W.
Pauli
in Ref. 6.8.
David
Bohm
, “A suggested interpretation of the quantum theory in terms of ‘hidden’ variables. I and II
,” Phys. Rev.
85
, 166
–179
(1952
).9.
Sir Edward
Appleton
et al, Scientific Papers Presented to Max Born
, (Hafner
, New York
, 1953
). I am very grateful to Arthur Fine for calling my attention to this book.10.
Reference 9, p.
14
.11.
See
W.
Eherenberg
and R. E.
Siday
, “The refractive index in electron optics and the principles of dynamics
,” Proc. Phys. Soc. London, Sect. B
62
, 8
–21
(1949
);Y.
Aharanov
and D.
Bohm
, “Significance of electromagnetic potential in quantum theory
,” Phys. Rev.
115
, 485
–491
(1959
). (The Eherenberg and Siday paper is concerned with the geometric optics of electrons. As an example, they consider the setup we describe with a magnetic field confined to a solenoid and a split electron beam passing around it. They show that the de Broglie waves are phase shifted by an amount that is proportional to the magnetic flux. They remark that it is curious that this phenomenon has to do with the flux and not a change of flux. The only use of the quantum theory in the paper is to assign de Broglie wave lengths to the electrons.)12.
J. J.
Sakurai
, Modern Quantum Mechanics
(Benjamin/Cummings
, Reading
, 1994
), pp. 136
–139
.13.
J. S.
Bell
(private communication).14.
David
Bohm
, “A suggested interpretation of the quantum theory in terms of `hidden variables’
,” Phys. Rev.
85
, 180
–193
(1952
).15.
16.
See Ref. 3, especially Chap. 22.
17.
I am pleased to acknowledge the help of Basil Hiley in preparing this appendix.
18.
Gary E.
Bowman
, “Bohmian mechanics as a heuristic device: Wave packets in the harmonic oscillator
,” Am. J. Phys.
70
, 313
–315
(2002
).© 2011 American Association of Physics Teachers.
2011
American Association of Physics Teachers
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