# On solutions of the Schrödinger equation with radiation conditions at infinity : the long-range case

Annales de l'institut Fourier (1999)

- Volume: 49, Issue: 5, page 1581-1602
- ISSN: 0373-0956

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topGâtel, Yannick, and Yafaev, Dimitri. "On solutions of the Schrödinger equation with radiation conditions at infinity : the long-range case." Annales de l'institut Fourier 49.5 (1999): 1581-1602. <http://eudml.org/doc/75394>.

@article{Gâtel1999,

abstract = {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.},

author = {Gâtel, Yannick, Yafaev, Dimitri},

journal = {Annales de l'institut Fourier},

keywords = {scattering theory; long-range potentials; homogeneous Schrödinger equation; class of solutions; scattering matrix},

language = {eng},

number = {5},

pages = {1581-1602},

publisher = {Association des Annales de l'Institut Fourier},

title = {On solutions of the Schrödinger equation with radiation conditions at infinity : the long-range case},

url = {http://eudml.org/doc/75394},

volume = {49},

year = {1999},

}

TY - JOUR

AU - Gâtel, Yannick

AU - Yafaev, Dimitri

TI - On solutions of the Schrödinger equation with radiation conditions at infinity : the long-range case

JO - Annales de l'institut Fourier

PY - 1999

PB - Association des Annales de l'Institut Fourier

VL - 49

IS - 5

SP - 1581

EP - 1602

AB - 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.

LA - eng

KW - scattering theory; long-range potentials; homogeneous Schrödinger equation; class of solutions; scattering matrix

UR - http://eudml.org/doc/75394

ER -

## References

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