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Mathematical surprises and Dirac's formalism in quantum mechanics

Abstract : Different formalisms are used in quantum mechanics for the description of states and observables: wave mechanics, matrix mechanics and the invariant formalism. We discuss the problems and shortcomings of the invariant formalism as well as those of the bra and ket notation introduced by Dirac in this context. We indicate how all problems can be solved or at least avoided. A series of examples illustrates the raised problems and shows how lack of mathematical concern can readily lead to surprising mathematical contradictions.
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http://hal.in2p3.fr/in2p3-00007666
Contributor : Sylvie Flores Connect in order to contact the contributor
Submitted on : Wednesday, February 14, 2001 - 11:18:00 AM
Last modification on : Friday, September 10, 2021 - 1:50:04 PM

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F. Gieres. Mathematical surprises and Dirac's formalism in quantum mechanics. Reports on Progress in Physics, IOP Publishing, 2000, 63, pp.1893-1931. ⟨10.1088/0034-4885/63/12/201⟩. ⟨in2p3-00007666⟩

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