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作者:Markus Faulhuber , Maurice A. de Gosson , David Rottensteiner
来源:[J].Applied and Computational Harmonic Analysis(IF 2.485), 2020, Vol.48 (1), pp.374-394Elsevier
摘要:Abstract(#br)Gaussian states are at the heart of quantum mechanics and play an essential role in quantum information processing. In this paper we provide approximation formulas for the expansion of a general Gaussian symbol in terms of elementary Gaussian functions. For this...
作者:Maurice A. de Gosson , Fabio Nicola
来源:[J].Bulletin des sciences mathématiques(IF 0.569), 2018, Vol.144, pp.64-81Elsevier
摘要:Abstract(#br)Quantization procedures play an essential role in operator theory, time–frequency analysis and, of course, in quantum mechanics. Roughly speaking the basic idea, due to Dirac, is to associate to any symbol, or observable, a ( x , ξ ) an operator Op ( a ) , accor...
作者:Maurice A. de Gosson
来源:[J].Physics Letters A(IF 1.766), 2017, Vol.381 (36), pp.3033-3037Elsevier
摘要:Abstract(#br)Recent cosmological measurements tend to confirm that the fine structure constant α is not immutable and has undergone a tiny variation since the Big Bang. Choosing adequate units, this could also reflect a variation of Planck's constant h . The aim of this Lett...
作者:Maurice A. de Gosson , Basil J. Hiley
来源:[J].Foundations of Physics(IF 1.17), 2011, Vol.41 (9), pp.1415-1436Springer
摘要:Abstract(#br)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 e...
作者:Maurice A. de Gosson
来源:[J].Applied and Computational Harmonic Analysis(IF 2.485), 2015, Vol.38 (2), pp.196-221Elsevier
摘要:Abstract(#br)Gabor frames can advantageously be redefined using the Heisenberg–Weyl operators familiar from harmonic analysis and quantum mechanics. Not only does this redefinition allow us to recover in a very simple way known results of symplectic covariance, but it immedi...
作者:Maurice A. de Gosson
来源:[J].Applied and Computational Harmonic Analysis(IF 2.485), 2015Elsevier
摘要:Abstract(#br)Hardy's uncertainty principle says that a square integrable function and its Fourier transform cannot be simultaneously arbitrarily sharply localized. We show that a multidimensional version of this uncertainty principle can be best understood in geometrical terms us...
作者:Maurice A. de Gosson
来源:[J].Journal of Geometry and Physics(IF 1.055), 2016, Vol.114Elsevier
摘要:Abstract(#br)We show, using a simple trick due to E. Fermi and rediscovered by Benenti and Strini, that to every Weyl–Heisenberg frame is associated in a canonical way a one-parameter group of symplectic transformations acting on the lattice of that frame without affecting t...
作者:Maurice A. de Gosson
来源:[J].Physics Reports(IF 22.929), 2016, Vol.623, pp.1-58Elsevier
摘要:Abstract(#br)The ordering problem has been one of the long standing and much discussed questions in quantum mechanics from its very beginning. Nowadays, there is more or less a consensus among physicists that the right prescription is Weyl’s rule, which is closely related to...
作者:Glen Dennis , Maurice A. de Gosson , Basil J. Hiley
来源:[J].Physics Letters A(IF 1.766), 2015, Vol.379 (18-19), pp.1224-1227Elsevier
摘要:Abstract(#br)We pursue our discussion of Fermi's surface initiated by Dennis, de Gosson and Hiley and show that Bohm's quantum potential can be viewed as an internal energy of a quantum system, giving further insight into its role in stationary states. This implies that the ...

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