On solutions of the Schrödinger equation with radiation conditions at infinity: the long-range case
Annales de l'Institut Fourier, Volume 49 (1999) no. 5, p. 1581-1602

We consider the homogeneous Schrödinger equation with a long-range potential and show that its solutions satisfying some a priori bound at infinity can asymptotically be expressed as a sum of incoming and outgoing distorted spherical waves. Coefficients of these waves are related by the scattering matrix. This generalizes a similar result obtained earlier in the short-range case.

Nous considérons l’équation de Schrödinger homogène avec un potentiel à longue portée et montrons que ses solutions satisfaisant une certaine borne a priori à l’infini peuvent s’exprimer asymptotiquement comme la somme d’ondes sphériques distordues rentrante et sortante. Les coefficients de ces ondes sont reliés par la matrice de la diffusion. Ceci généralise un résultat similaire précédemment établi pour un potentiel à courte portée

@article{AIF_1999__49_5_1581_0,
     author = {G\^atel, Yannick and Yafaev, Dimitri},
     title = {On solutions of the Schr\"odinger equation with radiation conditions at infinity: the long-range case},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {49},
     number = {5},
     year = {1999},
     pages = {1581-1602},
     doi = {10.5802/aif.1730},
     zbl = {0939.35050},
     mrnumber = {2000m:35044},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1999__49_5_1581_0}
}
On solutions of the Schrödinger equation with radiation conditions at infinity: the long-range case. Annales de l'Institut Fourier, Volume 49 (1999) no. 5, pp. 1581-1602. doi : 10.5802/aif.1730. http://www.numdam.org/item/AIF_1999__49_5_1581_0/

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