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- Title
Scattering Problem of Three One-Dimensional Quantum Particles. Case of Repulsive Coulomb Pair Potentials at Large Distances.
- Authors
Budylin, A. M.; Levin, S. B.
- Abstract
The present paper considers the quantum scattering problem for three one-dimensional particles with pair Coulomb repulsion potentials at large distances. The coordinate asymptotics of the resolvent kernel in the so-called BBK domain is calculated, which allows a reduction to the already solved scattering problem with short-range potentials. Based on this reduction, the coordinate asymptotics of the resolvent kernel is constructed in the entire configuration space when the spectral parameter falls on an absolutely continuous spectrum. The resulting formulas make it possible to rigorously justify the coordinate asymptotics of wave functions of an absolutely continuous spectrum obtained in the frame of the diffraction approach.
- Subjects
COULOMB potential; QUANTUM scattering; CONFIGURATION space; WAVE functions; CONTINUOUS functions; SCHRODINGER operator; INVERSE scattering transform
- Publication
Journal of Mathematical Sciences, 2023, Vol 277, Issue 4, p533
- ISSN
1072-3374
- Publication type
Article
- DOI
10.1007/s10958-023-06860-w