56 citations · 520 across the 52 of their papers we have counts for
5 papers · 1 filter
Quantum Indeterminacy, Polar Duality, and Symplectic Capacities
Maurice A. de Gosson
The notion of polarity between sets, well-known from convex geometry, is a geometric version of the Fourier transform. We exploit this analogy to propose a new simple definition of…
Maximal Covariance Group of Wigner Transforms and Pseudo-Differential Operators
Nuno Costa Dias, Maurice A. de Gosson, João Nuno Prata
We show that the linear symplectic and anti-symplectic transformations form the maximal covariance group for both the Wigner transform and Weyl operators. The proof is based on a n…
Symplectic and Hamiltonian Deformations of Gabor Frames
Maurice A. de Gosson
We study symplectic deformations of Gabor frames using the covariance properties of the Heisenberg operators. This allows us to recover in a very simple way known results. We there…
Short Time Quantum Propagator and Bohmian Trajectories
Maurice de Gosson, Basil Hiley
We begin by giving correct expressions for the short-time action; following the work of one of us and Makri--Miller. We use these estimates to derive a correct expression modulo mo…
Born-Jordan Quantization and the Uncertainty Principle
Maurice A. de Gosson
The Weyl correspondence and the related Wigner formalism lie at the core of traditional quantum mechanics. We discuss here an alternative quantization scheme, whose idea goes back…