How probability arises in quantum mechanics

Journal Article · Thu Jun 01 04:00:00 UTC 1989 · Annals of Physics (New York); (USA)

DOI:https://doi.org/10.1016/0003-4916(89)90141-3· OSTI ID:5397556

Farhi, E; Goldstone, J ^[1]; Gutmann, S ^[2]

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1. Center for Theoretical Physics, Laboratory for Nuclear Science and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (US)
2. Department of Mathematics, Northeastern University, Boston, Massachusetts 02115

A version of the postulates of quantum mechanics is presented in which no reference is made to probability. Instead we rely on a weaker postulate referring to eigenvalues and eigenstates. The modulus squared of the inner product of two state vectors is shown to be an eigenvalue of the operator representing a {ital frequency} measurement on the system of an infinite number of copies of the original system. The argument makes essential use of the Strong Law of Large numbers. {copyright} 1989 Academic Press, Inc.

• OSTI ID: 5397556
• Journal Information: Annals of Physics (New York); (USA), Journal Name: Annals of Physics (New York); (USA) Vol. 192:2; ISSN 0003-4916; ISSN APNYA
• Country of Publication: United States
• Language: English

Related Subjects

657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BANACH SPACE
EIGENSTATES
EIGENVALUES
HERMITIAN OPERATORS
HILBERT SPACE
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
MECHANICS
PROBABILITY
QUANTUM MECHANICS
SPACE