On applications of Maupertuis-Jacobi correspondence for Hamiltonians F(x,|p|) in some 2-D stationary semiclassical problems

2014/09/10 by Dobrokhotov, S., Minenkov, D., Rouleux, M.
#FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1409.3170

Abstract

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 Schrödinger equation, the 2-D Dirac equation for graphene and linear water wave theory.

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