Titlebook: Born-Jordan Quantization; Theory and Applicati Maurice A. de Gosson Book 2016 Springer International Publishing Switzerland 2016 Grossmann-

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Einleitung: OrientierungsmittelIn this chapter we initiate the study of continuity properties for Born–Jordan operators. We will discuss the global symbol classes introduced by Shubin; they are “global” in the sense that they satisfy growth estimates with an equal weighting on the position and momentum variables.

Anthem

Introduction,December 14, 1900, is usually regarded as the official date of birth of quantum theory, because on that day Max Planck presented a memoir at a meeting of the Physical Society of Berlin in which he solved the enigma of the blackbody spectrum by introducing a new, fundamental, constant of Nature.

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On the Quantization ProblemIn 1925 Max Born and Pascual Jordan set out to give a rigorous mathematical basis to Werner Heisenberg’s newly born “matrix mechanics”. This led them led to state a quantization rule for monomials.

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Quantization of MonomialsIn this chapter we begin by collecting some facts about the quantization of monomials and polynomials, with a particular emphasis on the Weyl and Born–Jordan schemes.

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The Weyl CorrespondenceThe Weyl correspondence, or Weyl quantization, is well-known both in harmonic analysis and quantum mechanics. It is part of the wider Weyl–Wigner–Moyal theory, where an emphasis on phase space techniques is made.

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Metaplectic OperatorsThe metaplectic group is a unitary representation of the double cover of the symplectic group; it is thus characterized by the exactness of the sequence.