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  1. The Symplectic Camel and the Uncertainty Principle: The Tip of an Iceberg? [REVIEW]Maurice A. de Gosson - 2009 - Foundations of Physics 39 (2):194-214.
    We show that the strong form of Heisenberg’s inequalities due to Robertson and Schrödinger can be formally derived using only classical considerations. This is achieved using a statistical tool known as the “minimum volume ellipsoid” together with the notion of symplectic capacity, which we view as a topological measure of uncertainty invariant under Hamiltonian dynamics. This invariant provides a right measurement tool to define what “quantum scale” is. We take the opportunity to discuss the principle of the symplectic camel, which (...)
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    Imprints of the Quantum World in Classical Mechanics.Maurice A. De Gosson & Basil J. Hiley - 2011 - Foundations of Physics 41 (9):1415-1436.
    The imprints left by quantum mechanics in classical (Hamiltonian) mechanics are much more numerous than is usually believed. We show that the Schrödinger equation for a nonrelativistic spinless particle is a classical equation which is equivalent to Hamilton’s equations. Our discussion is quite general, and incorporates time-dependent systems. This gives us the opportunity of discussing the group of Hamiltonian canonical transformations which is a non-linear variant of the usual symplectic group.
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    Quantum Blobs.Maurice A. De Gosson - 2013 - Foundations of Physics 43 (4):440-457.
    Quantum blobs are the smallest phase space units of phase space compatible with the uncertainty principle of quantum mechanics and having the symplectic group as group of symmetries. Quantum blobs are in a bijective correspondence with the squeezed coherent states from standard quantum mechanics, of which they are a phase space picture. This allows us to propose a substitute for phase space in quantum mechanics. We study the relationship between quantum blobs with a certain class of level sets defined by (...)
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    Clifford Algebras in Symplectic Geometry and Quantum Mechanics.Ernst Binz, Maurice A. De Gosson & Basil J. Hiley - 2013 - Foundations of Physics 43 (4):424-439.
    The necessary appearance of Clifford algebras in the quantum description of fermions has prompted us to re-examine the fundamental role played by the quaternion Clifford algebra, C 0,2 . This algebra is essentially the geometric algebra describing the rotational properties of space. Hidden within this algebra are symplectic structures with Heisenberg algebras at their core. This algebra also enables us to define a Poisson algebra of all homogeneous quadratic polynomials on a two-dimensional sub-space, $\mathbb{F}^{a}$ of the Euclidean three-space. This enables (...)
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    The Angular Momentum Dilemma and Born–Jordan Quantization.Maurice A. De Gosson - 2017 - Foundations of Physics 47 (1):61-70.
    The rigorous equivalence of the Schrödinger and Heisenberg pictures requires that one uses Born–Jordan quantization in place of Weyl quantization. We confirm this by showing that the much discussed “ angular momentum dilemma” disappears if one uses Born–Jordan quantization. We argue that the latter is the only physically correct quantization procedure. We also briefly discuss a possible redefinition of phase space quantum mechanics, where the usual Wigner distribution has to be replaced with a new quasi-distribution associated with Born–Jordan quantization, and (...)
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    Born–Jordan Quantization and the Equivalence of the Schrödinger and Heisenberg Pictures.Maurice A. de Gosson - 2014 - Foundations of Physics 44 (10):1096-1106.
    The aim of the famous Born and Jordan 1925 paper was to put Heisenberg’s matrix mechanics on a firm mathematical basis. Born and Jordan showed that if one wants to ensure energy conservation in Heisenberg’s theory it is necessary and sufficient to quantize observables following a certain ordering rule. One apparently unnoticed consequence of this fact is that Schrödinger’s wave mechanics cannot be equivalent to Heisenberg’s more physically motivated matrix mechanics unless its observables are quantized using this rule, and not (...)
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