The quantum probability calculus. (English) Zbl 0342.60004


60A05 Axioms; other general questions in probability
60K35 Interacting random processes; statistical mechanics type models; percolation theory
03B99 General logic
06C15 Complemented lattices, orthocomplemented lattices and posets
47A99 General theory of linear operators
Full Text: DOI


[1] Belinfante, F. J., A Survey of Hidden Variable Theories, Pergamon Press, New York, 1973.
[2] Brittin, W. E. and Chappell, W. R., ?The Wigner Distribution Function and Second Quantization in Phase Space?, Review of Modern Physics 34 (1962), 620-627. · Zbl 0113.45705
[3] Gleason, A. M., ?Measures on the Closed Subspaces of a Hilbert Space?, Journal of Mathematics and Mechanics 6 (1957), 885-893. · Zbl 0078.28803
[4] Gudder, S. P., ?Hilbert Space, Independence, and Generalized Probability?, Journal of Mathematical Analysis and Applications 20 (1967), 48-61. · Zbl 0171.15602
[5] Gudder, S. P., ?Joint Distributions of Observables?, Journal of Mathematics and Mechanics 18 (1968), 325-335. · Zbl 0241.60092
[6] Gudder, S. P. and Marchand, J. P., ?Non-Commutative Probability on von Neumann Algebras?, Journal of Mathematical Physics 13 (1972), 799-806. · Zbl 0232.46064
[7] Gudder, S. P. and Piron, C., ?Observables and the Field in Quantum Mechanics?, Journal of Mathematical Physics 12 (1971), 1583-1588. · Zbl 0281.06005
[8] Jauch, J. M., Foundations of Quantum Mechanics, Addison-Wesley, Reading, 1968. · Zbl 0166.23301
[9] Kolmogorov, A. N., Foundations of the Theory of Probability, Chelsea, New York, 1956, transl. and ed. by N. Morrison. · Zbl 0074.12202
[10] Moyal, J. E., ?Quantum Mechanics as a Statistical Theory?, Proceedings of the Cambridge Philosophical Society 45 (1949), 99-124. · Zbl 0031.33601
[11] Park, J. L. and Margenau, H., ?Simultaneous Measurability in Quantum Theory?, International Journal of Theoretical Physics 1 (1968), 211-282.
[12] Piron, C., ?Axiomatique Quantique?, Helvetica Physica Acta 37 (1964), 439-467.
[13] Renyi, A., Probability Theory, North Holland, Amsterdam, 1970. · Zbl 0245.60002
[14] Suppes, P., ?Probability Concepts in Quantum Mechanics?, Philosophy of Science 28 (1961), 378-389.
[15] Suppes, P., ?The Role of Probability in Quantum Mechanics? in B. Baumrin (ed.), Philosophy of Science, The Delaware Seminar, Wiley, New York, 1963.
[16] Suppes, P., ?The Probabilistic Argument for a Non-classical Logic of Quantum Mechanics?, Philosophy of Science 33 (1966), 14-21.
[17] Varadarajan, V. S., ?Probability in Physics and a Theorem on Simultaneous Observability?, Comments on Pure and Applied Mathematics 15 (1962), 189-216. · Zbl 0109.44705
[18] Wigner, E., ?On the Quantum Theory for Thermodynamic Equilibrium?, Physical Review 40 (1932), 749-759. · JFM 58.0948.07
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