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On wave functions in quantum mechanics. I

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On wave functions in quantum mechanics. I RENDICONTI del SEMINARIO MATEMATICO della UNIVERSITÀ DI PADOVA A. BRESSAN Onwave functions in quantummechanics. I Rendiconti del Seminario Matematico della Università di Padova, tome 60 (1978), p. 77-98. <> © Rendiconti del Seminario Matematico della Università di Padova, 1978, tous droits réservés. L’accès aux archives de la revue « Rendiconti del Seminario Matematico della Università di Padova » ( implique l’ac- cord avec les conditions générales d’utilisation ( php). Toute utilisation commerciale ou impression systématique est consti- tutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques On Wave Functions in Quantum Mechanics. I. A. BRESSAN (*) Present experiments are compatible with the possibility P of determining quantistic states by the expectations of fundamental observ- ables-í.e. observables that are measurable with arbitrary precision. More is often assumed to prove Theor 2.1, the fundamental proportionality property of the w ave functions of a same state; for this aim some axioms not only unsatisfactorily supported but even disproved by to-day experi- ments were, and for simplicity reasons are still assumed. In Part 1 Theor 2.1 is deduced from Post 4.1, a postulate much weaker than P on the state y+ immediately after a measurement. Furthermore the observables used in its proof as fundamental, are surely so in that an ideal apparatus to measure them has been exhibited. In addition some well known postulates related with Post 4.1 are discussed and Post 4.1 is justified (on the basis of widely used postulates). In Part 2 the denial of ~ is supported and in Part 3 an a,giomatíc theory, of quantum mechanics is introduced, in whi

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