Lagrangian manifolds related to the asymptotics of Hermite polynomials

DOI10.1134/S0001434618110263zbMath1409.42019OpenAlexW2908390790WikidataQ128674016 ScholiaQ128674016MaRDI QIDQ668310

S. Yu. Dobrokhotov, Anna V. Tsvetkova

Publication date: 19 March 2019

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0001434618110263

zbMATH Keywords

asymptoticsSchrödinger equationfinite-difference equationHermite polynomialLagrangian manifoldMaslov canonical operator

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05)

Related Items (13)

Asymptotics of multiple orthogonal Hermite polynomials \(H_{n_1,n_2}(z,\alpha)\) determined by a third-order differential equation ⋮ Complex WKB method for a system of two linear difference equations ⋮ Plancherel–Rotach type asymptotic formulae for multiple orthogonal Hermite polynomials and recurrence relations ⋮ Global asymptotics for functions of parabolic cylinder and solutions of the Schrödinger equation with a potential in the form of a nonsmooth double well ⋮ Complex WKB method (one-dimensional linear problems on the complex plane) ⋮ Efficient formulas for the Maslov canonical operator near a simple caustic ⋮ Airy functions and transition between semiclassical and harmonic oscillator approximations for one-dimensional bound states ⋮ Asymptotic eigenfunctions of the ``bouncing ball type for the two-dimensional Schrödinger operator with a symmetric potential ⋮ An approach to finding the asymptotics of polynomials given by recurrence relations ⋮ Representation of Bessel functions by the Maslov canonical operator ⋮ WKB asymptotics of meromorphic solutions to difference equations ⋮ The Complex WKB Method for Difference Equations and Airy Functions ⋮ Difference equations in the complex plane: quasiclassical asymptotics and Berry phase

Cites Work

• Asymptotics of wave functions of the stationary Schrödinger equation in the Weyl chamber
• Plancherel-Rotach type asymptotics for solutions of linear recurrence relations with rational coefficients
• Complex WKB method for a difference Schrödinger equation with the potential being a trigonometric polynomial
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