123 citations · 1k across the 65 of their papers we have counts for
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Quantum mechanics in phase space: The Schrödinger and the Moyal representations
Nuno Costa Dias, Maurice de Gosson, Franz Luef +1
We present a phase space formulation of quantum mechanics in the Schrödinger representation and derive the associated Weyl pseudo-differential calculus. We prove that the resulting…
A pseudo-differential calculus on non-standard symplectic space; spectral and regularity results in modulation spaces
Nuno Costa Dias, Maurice de Gosson, Franz Luef +1
The usual Weyl calculus is intimately associated with the choice of the standard symplectic structure on . In this paper we will show that the r…
A global, dynamical formulation of quantum confined systems
Nuno Costa Dias, João Nuno Prata
A brief review of some recent results on the global self-adjoint formulation of systems with boundaries is presented. We specialize to the 1-dimensional case and obtain a dynamical…
A symplectic extension map and a new Shubin class of pseudo-differential operators
Nuno Costa Dias, Maurice A. de Gosson, João Nuno Prata
For an arbitrary pseudo-differential operator with Weyl symbol $a\in\mathcal{S}^{\prime}(\mathb…
Noncommutative Graphene
C. Bastos, O. Bertolami, N. Dias +1
We consider a noncommutative description of graphene. This description consists of a Dirac equation for massless Dirac fermions plus noncommutative corrections, which are treated i…
Violation of the Robertson-Schrödinger uncertainty principle and non-commutative quantum mechanics
Catarina Bastos, Orfeu Bertolami, Nuno Costa Dias +1
We show that a possible violation of the Robertson-Schrödinger uncertainty principle may signal the existence of a deformation of the Heisenberg-Weyl algebra. More precisely, we pr…