The Maupertuis-Jacobi principle for Hamiltonians of the form F(x, |p|) in two-dimensional stationary semiclassical problems - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Matematicheskie Zametki / Mathematical Notes Année : 2015

The Maupertuis-Jacobi principle for Hamiltonians of the form F(x, |p|) in two-dimensional stationary semiclassical problems

Résumé

We make use of the Maupertuis -- Jacobi correspondence, well known in Classical Mechanics, to simplify 2-D asymptotic formulas based on Maslov's canonical operator, when constructing Lagrangian manifolds invariant with respect to phase flows for Hamiltonians of the form $F(x,|p|)$. As examples we consider Hamiltonians coming from the Schr\"odinger equation, the 2-D Dirac equation for graphene and linear water wave theory.

Dates et versions

hal-01264841 , version 1 (29-01-2016)

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Citer

S. Dobrokhotov, D. Minenkov, M. Rouleux. The Maupertuis-Jacobi principle for Hamiltonians of the form F(x, |p|) in two-dimensional stationary semiclassical problems. Matematicheskie Zametki / Mathematical Notes, 2015, 97 (1), pp.42-49. ⟨10.1134/S0001434615010058⟩. ⟨hal-01264841⟩
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