Geodesic
On the scattering theory of the Laplacian with a periodic boundary condition. I. Existence of wave operators
Documenta mathematica, Tome 8 (2003), pp. 547-565
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We study spectral and scattering properties of the Laplacian H(σ)=−Δ in L2​(R+2​) corresponding to the boundary condition ∂ν∂u​+σu=0 for a wide class of periodic functions σ. The Floquet decomposition leads to problems on an unbounded cell which are analyzed in detail. We prove that the wave operators W±​(H(σ),H(0)) exist.
DOI : 10.4171/dm/150
Classification : 35J10, 35J25, 35P05, 35P25
Mots-clés : Schrödinger operator, singular potential, scattering theory, periodic operator 
@article{10_4171_dm_150,
     author = {Rupert L. Frank},
     title = {On the scattering theory of the {Laplacian} with a periodic boundary condition. {I.} {Existence} of wave operators},
     journal = {Documenta mathematica},
     pages = {547--565},
     year = {2003},
     volume = {8},
     doi = {10.4171/dm/150},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/150/}
}
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Rupert L. Frank. On the scattering theory of the Laplacian with a periodic boundary condition. I. Existence of wave operators. Documenta mathematica, Tome 8 (2003), pp. 547-565. doi: 10.4171/dm/150

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