The concept of probability played an important role in the very beginning of ► quantum theory, when Max Planck (1858–1947) postulated the discrete emission and absorption of radiation in a ► black body radiation. The quantum statistical mechanics developed by Planck and his successors has extraordinary consequences treated elsewhere in this Compendium. Here, however, the emphasis will be upon the unprecedented role of probability in the quantum mechanical treatment of the state of a physical system, which will be discussed first in the ► wave mechanical formulation of Schrodinger, and then in the more abstract and general ► Hilbert space formulation.
The thesis of Louis de Broglie (1892–1987) of 1924 [1] postulated that waves are associated with ► electrons and that a discrete atomic state is determined by the occurrence of an integral number of wave lengths in a circular trajectory about the atomic nucleus. Erwin Schrodinger (1887–1961) [2] systematized and generalized de Broglie's idea in the first of his series of papers on ► wave mechanics.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Primary Literature
L. de Broglie: Thèses présentées à la Faculté des Sciences de l'Université de Paris (Masson et Cie., Paris 1924)
E. Schrödinger: Quantisierung als Eigenwertproblem. Annalen d. Physik 79, 361 (1926). Reprinted, as are [3] and [4], in E. Schrödinger, Abhandlungen zur Wellenmechanik (J.A. Barth. Leipzig. 1926), translated as Collected Papers on Wave Mechanics by J.F. Shearer and W.M. Deans (Blackie & Son, London/Glasgow, 1928)
E. Schrödinger: Quantisierung als Eigenwertproblem. Second communication, Annalen d. Physik 79, 489 (1926); third communication, Annalen d. Physik 80, 437 (1926); fourth communication, Annalen d. Physik 81, 109 (1926)
E. Schrödinger: Über das Verhältnis der Heisenberg-Born-Jordanschen Quantenmechanik zu der meinen. Annalen d. Physik 79, 734 (1926)
W. Heisenberg: Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen. Zeitschrift f. Physik 33, 879 (1925).
E. Schrödinger: Quantisierung als Eigenwertproblem. Fourth communication, reference [3].
M. Born: Quantenmechanik der Stossvorgänge. Zeitschrift f. Physik 38, 803 (1926)
F. London: Winkelvariable und kanonische Transformationen in der Undulationsmechanik. Zeitchrifts f. Physik 40, 193 (1926)
P.A.M. Dirac: The physical interpretation of the quantum dynamics. Proceedings of the Royal Society of London A, 113, 621 (1926). Also The Principles of Quantum Mechanics (Clarendon Press, Oxford, 1930) and three subsequent editions.
G. Mackey: Induced Representations of Groups and Quantum Mechanics (W.A, Benjamin, New York, 1968, chapters 2–3)
D. Hilbert, J. von Neumann, and L. Nordheim: Über die Grundlagen der Quantenmechanik. Mathematische Annalen 98, 1 (1927)
J. von Neumann: Mathematische Grundlagen der Quantenmechanik (Springer, Berlin 1932); transl. as Mathematical Foundations of Quantum Mechanics by R.T. Beyer (Princeton University Press, Princeton 1955)
G. Birkhoff and J. von Neumann: The logic of quantum mechanics. Annals of Mathematics 37, 823 (1936)
C. Piron: Foundations of Quantum Physics (W.A. Benjamin, Reading MA, 1976, 6–9)
G. Mackey: Mathematical Foundations of Quantum Mechanics (W.A. Benjamin, New York 1964, 61–73)
V.S. Varadarajan: Geometry of Quantum Theory (van Nostrand, Princeton 1968, 8–11)
G. Mackey: Ref. 15, p. 71.
A.M. Gleason: Measures on the closed subspaces of a Hilbert space. J. Mathematics and Mechanics 6, 885 (1957)
W. Heisenberg: Physics and Philosophy (Harper, New York, 1962, 54, 185)
Secondary Literature
M. Jammer: The Conceptual Development of Quantum Mechanics (McGraw-Hill, New York 1966, 293–322)
S.-I. Tomonaga: Quantum Mechanics, vol. II (North-Holland, Amsterdam 1966, chap. 8, pp. 163–200; chap. 9, pp. 276–287)
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Shimony, A. (2009). Probability in Quantum Mechanics. In: Greenberger, D., Hentschel, K., Weinert, F. (eds) Compendium of Quantum Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70626-7_149
Download citation
DOI: https://doi.org/10.1007/978-3-540-70626-7_149
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-70622-9
Online ISBN: 978-3-540-70626-7
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)