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Prog. Theor. Phys. Vol. 25 No. 5 (1961) pp. 743-752
On an Extension of the Mathematical Framework of the Quantum Theory
Hitoshi Wakita
Research Institute for Theoretical Physics, Hiroshima University, Takehara, Hiroshima-ken
(Received December 28, 1960)
Abstract:
Extending the usual framework of the quantum theory, we have succeeded in gettig a new mathematical framework. The most essential character of the usual theory is preserved in the new theory, that is, the set of physical quantities can be represented by an operator algebra in a separable Hilbert space. In the new theory, on the other hand, we can rigorously treat the interaction Hamiltonians, which cannot be treated in the usual framework. In our new framework there are always solutions of the Schrödinger equation for any Hamiltonian. However, the most serious defect of our theory is in the fact that we have no guarantee of the uniqueness of solutions.
URL :
http://ptp.ipap.jp/link?PTP/25/743/
DOI : 10.1143/PTP.25.743
References:
- E. Hille and R. S. Phillips, Functional Analysis and Semi-Groups (Ammer. Math. Soc. Colloq. Publ., New York, 1957).
- H. Wakita, Prog. Theor. Phys. 20 (1958), 35[PTP]; ibid. 21 (1959), 299[PTP].
- J. Dixmier, Les algèbres d'opérateurs dans l'espace hilbertien (Gauthier-Villars, Paris, 1957).
- Z. Takeda, Proc. Jpn. Acad. 30 (1954), 299.
- S. Banach, Théorie des opérations linéaires (Warsaw, 1932).
- N. Bourbaki, Espaces vectoriels topologiques, Chap. I, II (Hermann, Paris, 1953).
- J. Dixmier, Ann. of Math. 51 (1950), 387.
Citing Article(s) :
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Progress of Theoretical Physics Vol. 28 No. 1 (1962) pp. 80-86
:
-
Mathematical Foundation of the Quantum Theory of Interacting Fields
-
Hitoshi Wakita
-
Progress of Theoretical Physics Vol. 28 No. 2 (1962) pp. 251-257
:
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On an Extension of the Mathematical Framework of the Quantum Theory. II
-
Hitoshi Wakita
