Abstract
A detailed list of postulates is formulated in an algebraic setting. These postulates are sufficient to entail the standard time evolution governed by the Schrödinger or Dirac equation. They are also necessary in a strong sense: Dropping any one of the postulates allows for other types of time evolution, as is demonstrated with examples. Some philosophical remarks hint on possible further investigations.
Similar content being viewed by others
References
M. Pavičić, “Bibliography on quantum logics and related structures,”Int. J. Theor. Phys. 31, 373–461 (1992).
R. Giles, “Foundations for quantum mechanics,” Ref. 21., pp. 277–322.
S. P. Gudder, “A survey of axiomatic quantum mechanics,” Ref. 21., pp. 323–363.
G. W. Mackey,The Mathematical Foundations of Quantum Mechanics (Benjamin, New York, (1963).
W. Thirring,A Course in Mathematical Physics 3: Quantum Mechanics of Atoms and Molecules (Springer, New York, 1981).
R. V. Kadison, “Transformations of states in operator theory and dynamics,”Topology 3,Suppl. 2, 177–198 (1965).
E. P. Wigner, “Group Theory and Its Application to the Quantum Mechanics of Atomic Spectra (Academic, New York, (1959).
W. Hunziker, “A note on symmetry operations in quantum mechanics,”Helv. Phys. Acta 45, 233–236 (1972).
J. von Neumann, “über einen Satz von Herrn M. H. Stone,”Ann. Math. (2) 33, 567–573 (1932).
M. Reed and B. Simon,Methods of Modern Mathematical Physics, Vol. 1 (Academic, New York, (1972).
M. Fannes and A. Verbeure, “On the time evolution automorphisms of the CCR-algebra for quantum mechanics,”Commun. Math. Phys. 35, 257–264 (1974).
S. Weinberg, “Precision tests of quantum mechanics,”Phys. Rev. Lett. 62, 485–488 (1989).
J. Polchinski, “Weinberg's nonlinear quantum mechanics and the Einstein-PodolskiRosen paradox,”Phys. Rev. Lett. 66, 397–400 (1991).
G. C. Ghirardi, A. Rimini, and T. Weber, “Unified dynamics for microscopic and macroscopic systems,”Phys. Rev. D 34, 470–479 (1986).
R. Solovay, “A model of set theory in Which every set of reals is Lebesgue-measurable,” 3Ann. Math. 92, 1–56 (1970).
E. Bishop,Foundations of Constructive Analysis (McGraw-Hill, New York, 1967).
P. J. Cohen, “The independence of the continuum hypothesis,”Proc. Natl. Acad. Sci. USA 50, 1143–48 (1963);ibid.,51, 105–110 (1964).
P. J. Cohen, “Comments on the foundation of set theory,” Ref. 20., pp. 9–11.
J. A. Wheeler, “Universe as home for man,”Am. Sci. 62, 683–691 (1974).
D. Scott, ed.:Axiomatic Set Theory. Proceedings of Symposia in Pure Mathematics,13, Vol. 1. (American Mathematical Society, Providence, Rhode Island, 1971).
C. A. Hooker, ed.:The Logico-Algebraic Approach to Quantum Mechanics (Reidel, Dordrecht, The Netherlands, 1979).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Baumgartner, B. Postulates for time evolution in quantum mechanics. Found Phys 24, 855–872 (1994). https://doi.org/10.1007/BF02067651
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02067651