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arXiv · 1409.3170

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

S. Dobrokhotov·D. Minenkov·M. Rouleux
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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 Schr\"odinger equation, the 2-D Dirac equation for graphene and linear water wave theory.

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S. Dobrokhotov, D. Minenkov, M. Rouleux. 2014-09-10. On applications of Maupertuis-Jacobi correspondence for Hamiltonians $F(x,|p|)$ in some 2-D stationary semiclassical problems. https://arxiv.org/abs/1409.3170

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