143 citations · 466 across the 10 of their papers we have counts for
10 papers
Faddeev-Jackiw Quantization of Non-Autonomous Singular Systems
Zahir Belhadi, Alain Bérard, Hervé Mohrbach
We extend the quantization à la Faddeev-Jackiw for non-autonomous singular systems. This leads to a generalization of the Schrödinger equation for those systems. The method is exem…
Quantization of soluble classical constrained systems
Zahir Belhadi, Ferhat Ménas, Alain Bérard +1
The derivation of the brackets among coordinates and momenta for classical constrained systems is a necessary step toward their quantization. Here we present a new approach for the…
Rational solutions for the Riccati-Schrödinger equations associated to translationally shape invariant potentials
Yves Grandati, Alain Bérard
We develop a new approach to build the eigenfunctions of a translationally shape-invariant potential. For this we show that their logarithmic derivatives can be expressed as termin…
Inverse problem and Bertrand's theorem
Yves Grandati, Alain Bérard, Ferhat Menas
The Bertrand's theorem can be formulated as the solution of an inverse problem for a classical unidimensional motion. We show that the solutions of these problems, if restricted to…
Semiclassical Dynamics of Dirac particles interacting with a Static Gravitational Field
Pierre Gosselin, Alain Bérard, Herve Mohrbach
The semiclassical limit for Dirac particles interacting with a static gravitational field is investigated. A Foldy-Wouthuysen transformation which diagonalizes at the semiclassical…
Spin Hall effect of Photons in a Static Gravitational Field
Pierre Gosselin, Alain Bérard, Herve Mohrbach
Starting from a Hamiltonian description of the photon within the set of Bargmann-Wigner equations we derive new semiclassical equations of motion for the photon propagating in stat…