Microlocal WKB expansions
نویسندگان
چکیده
منابع مشابه
Virtual turning points and bifurcation of Stokes curves for higher order ordinary differential equations
For a higher order linear ordinary differential operator P , its Stokes curve bifurcates in general when it hits another turning point of P . This phenomenon is most neatly understandable by taking into account Stokes curves emanating from virtual turning points, together with those from ordinary turning points. This understanding of the bifurcation of a Stokes curve plays an important role in ...
متن کاملar X iv : h ep - t h / 01 09 18 5 v 3 2 0 N ov 2 00 1 Once again : Instanton method vs . WKB
A recent analytic test of the instanton method performed by comparing the exact spectrum of the Lamé potential (derived from representations of a finite dimensional matrix expressed in terms of su(2) generators) with the results of the tight–binding and instanton approximations as well as the standard WKB approximation is commented upon. It is pointed out that in the case of the Lamé potential ...
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A new semiclassical approach to the linear and nonlinear one-dimensional Schrödinger equation is presented. For both equations our zeroth-order solutions include nonperturbative quantum corrections to the WKB solution and the Thomas-Fermi solution, thereby allowing us to make uniformly converging perturbative expansions of the wave functions. Our method leads to a new quantization condition tha...
متن کاملar X iv : h ep - t h / 01 09 18 5 v 2 9 N ov 2 00 1 Once again : Instanton method vs . WKB
A recent analytic test of the instanton method performed by comparing the exact spectrum of the Lamé potential (derived from representations of a finite dimensional matrix expressed in terms of su(2) generators) with the results of the tight–binding and instanton approximations as well as the standard WKB approximation is commented upon. It is pointed out that in the case of the Lamé potential ...
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with our sincerest congratulations on his being awarded Prix de l’Etat (Academie des Science). One of the central issues of this article is the introduction of the notion of virtual turning points for higher order Painlevé equations, and two of the authors (Kawai and Takei), together with T. Aoki, fondly remember the stimulating and comfortable conference (Algebraic analysis of singular perturb...
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