M. Rouleux

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20242026

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math-ph2026

Asymptotic solutions: glancing trajectories, Lagrangian singularities, and Bessel cylinders

Ilya Bogaevskii, Michel Rouleux

We find a normal form for the simplest Lagrangian singularity appearing as the projection onto the space-energy of a solution to the Hamilton-Jacobi equation. Using this normal for…

math-ph2026

The flux norm, Bohr-Sommerfeld Quantization Rules and the scattering problem for h $I^¨$ DO's on the real line

Abdelwaheb Ifa, Michel Rouleux

We revisit the well known Bohr-Sommerfeld quantization rule (BS) of order 2 for a self-adjoint 1-D h-Pseudo-differential operator within the algebraic and microlocal framework of H…

math-ph2024

Generalized exchange operators for a system of spin-1 particles

Charlie Jeudy, Michel Rouleux

The irreps $(S U (2), H, U)$ of SU(2) of dimension $(2 S + 1)^{N}$ , i.e. operators acting on the space $H = H_{N} = C^{(2 S + 1)^{N}}$ of $N$ identical particles with spin $…

Asymptotic solutions: glancing trajectories, Lagrangian singularities, and Bessel cylinders

The flux norm, Bohr-Sommerfeld Quantization Rules and the scattering problem for h I^¨DO's on the real line

Generalized exchange operators for a system of spin-1 particles

The flux norm, Bohr-Sommerfeld Quantization Rules and the scattering problem for h $I^¨$ DO's on the real line