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by n4r9
1558 days ago
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> By the time von
Neumann started his investigations on the formal framework of
quantum mechanics this theory was known in two different mathe-
matical formulations: the "matrix mechanics" of Heisenberg, Born
and Jordan, and the "wave mechanics" of Schrödinger. The mathe-
matical equivalence of these formulations had been established by
Schrödinger, and they had both been embedded as special cases in a
general formalism, often called "transformation theory," developed
by Dirac and Jordan. This formalism, however, was rather clumsy
and it was hampered by its reliance upon ill-defined mathematical
objects, the famous delta-functions of Dirac and their derivatives.
Although von Neumann himself attempted at first, in collaboration
with Hilbert and Nordheim [l], to edify the quantum-mechanical formalism along similar lines, he soon realized that a much more
natural framework was provided by the abstract, axiomatic theory of
Hilbert spaces and their linear operators [2], This mathematical
formulation of quantum mechanics, whereby states of the physical
system are described by Hilbert space vectors and measurable quan-
tities by hermitian operators acting upon them, has been very suc-
cessful indeed. Unchanged in its essentials it has survived the two
great extensions which quantum theory was to undergo soon: the
relativistic quantum mechanics of particles (Dirac equation) and the
quantum theory of fields. Leon van Hove, "Von Neumann's Contributions to Quantum Mechanics", 1958 https://www.ams.org/journals/bull/1958-64-03/S0002-9904-1958... |
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