Abstract
A realistic axiomatic formulation of nonrelativistic quantum mechanics for a single microsystem with spin is presented, from which the most important theorems of the theory can be deduced. In comparison with previous formulations, the formal aspect has been improved by the use of certain mathematical theories, such as the theory of rigged spaces, and group theory. The standard formalism is naturally obtained from the latter, starting from a central primitive concept: the Galilei group.
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References
Bargmann, V. (1954).Annals of Mathematics,59, 1.
Bunge, M. (1967).Foundations of Physics, Springer-Verlag, Berlin.
Bunge, M. (1967). A ghost-free axiomatization of quantum mechanics, inQuantum Theory and Reality, M. Bunge, ed., Springer-Verlag, Berlin.
Bunge, M. (1973).Philosophy of Physics, Reidel, Dordrecht.
Bunge, M. (1974).Sense and Reference, Reidel, Dordrecht.
Bunge, M. (1974).Interpretation and Truth, Reidel, Dordrecht.
Cini, M. (1983).Nuovo Cimento B,73, 27.
Gel'fand, I. M., and Shilov, G. E. (1967).Generalized Functions, Vol. 3, Academic Press, New York.
Gel'fand, I. M.,et al. (1964–1968).Generalized Functions, Vols. 1–4, Academic Press, New York.
Hamermesh, M. (1960).Annals of Physics,9, 518.
Inönu, E., and Wigner, E. P. (1952).Nuovo Cimento,9, 705.
Jones, D. S. (1966).Generalised Functions, McGraw-Hill, London.
Lèvy-Leblond, J. M. (1963).Journal of Mathematical Physics,4, 776.
Lèvy-Leblond, J. M. (1967).Communications in Mathematical Physics,4, 157.
Popper, K. R. (1959).British Journal for the Philosophy of Science,10, 25.
Von Neumann, J. (1955).Mathematical Foundations of Quantum Mechanics, Princeton University Press, Princeton, New Jersey.
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Perez Bergliaffa, S.E., Vucetich, H. & Romero, G.E. Axiomatic foundations of nonrelativistic quantum mechanics: A realistic approach. Int J Theor Phys 32, 1507–1522 (1993). https://doi.org/10.1007/BF00672852
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DOI: https://doi.org/10.1007/BF00672852