The term observable has become the standard name in quantum mechanics for what used to be called physical quantity or measurable quantity in classical physics. This term derives from observable quantity (“beobachtbare Grösse”), which was used by Werner Heisenberg in his groundbreaking work on ► matrix mechanics [1] to emphasize that the meaning of a physical quantity must be specified by means of an operational definition. Together with a state (► states in quantum mechanics), an observable determines the probabilities of the possible outcomes of a measurement of that observable on the quantum system prepared in the given state. Conversely, observables are identified by the totalities of their measurement outcome probabilities. Examples of observables in quantum mechanics are position, velocity, momentum, angular momentum, spin, and energy. ► Spin; Stern-Gerlach experiment; Vector model.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Primary Literature
Heisenberg, W.: Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen. Zeitschrift für Physik 33 879–893 (1925).
Born, M.: Zur Quantenmechanik der Stoßvorgänge. Zeitschrift für Physik 37, 863–867 (1926).
von Neumann, J.: Mathematische Begründung der Quantenmechanik. Göttinger Nachrichten 1–57 (1927). Wahrscheinlichkeitstheoretischer Aufbau der Quantenmechanik. G öttinger Nachrichten 245–272 (1927). Allgemeine Eigenwerttheorie Hermitescher Funktionaloperatoren, Mathematische Annalen 102, 49–131 (1929). This all is summarized in his book Mathematische Grundlagen der Quantenmechanik (Springer, Berlin 1932, 2nd ed. 1996); English translation (by R. Beyer): Mathematical Foundations of Quantum Mechanics (Princeton University Press, Princeton 1955).
Heisenberg, W.: Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik. Zeitschrift für Physik 43, 172–198 (1927).
von Neumann, J.: Über Funktionen von Funktionaloperatoren. Annals of Mathematics 32, 191–226 (1931).
Ludwig, G.: Versuch einer axiomatischen Grundlegung der Quantenmechanik und allgemeinerer physikalischer Theorien. Zeitschrift für Physik 181 233–260 (1964).
Davies, E.B., J.T. Lewis: An Operational Approach to Quantum Probability. Communication in Mathematical Physics 17, 239–260 (1970).
Secondary Literature
Davies, E.B.: Quantum Theory of Opens Systems (Academic, New York 1976).
Berberian, S.K.: Notes on Spectral Theory (D. van Nostrand, Princeton 1966).
Helstrom, C.W.: Quantum Detection and Estimation Theory (Academic, New York 1976).
Holevo, A.S.: Probabilistic and Statistical Aspects of Quantum Theory (North Holland, Amsterdam 1982).
Ludwig, G.: Foundations of Quantum Mechanics (Springer, Berlin 1983).
Kraus, K.: States, Effects, and Operations (Springer, Berlin 1983).
Busch, P., T. Heinonen, P. Lahti: Heisenberg's Uncertainty Principle, Physics Reports 452 (2007) 155–176.
Busch, P., M. Grabowski, P. Lahti: Operational Quantum Physics, Springer, LNP m31, 1995, 2nd Corrected Printing 1997.
Peres, A.: Quantum Theory: Concepts and Methods (Kluwer, Dordrecht 1993).
Nielsen, M.A., I.L.Chuang: Quantum Computation and Quantum Information (Cambridge University Press, Cambridge 2000).
Stenholm, S., K.-A. Suominen: Quantum Approach to Information (Wiley, New York 2005).
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Busch, P., Lahti, P. (2009). Observable. 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_130
Download citation
DOI: https://doi.org/10.1007/978-3-540-70626-7_130
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)