Geodesic
Reformulation of the Lax--Phillips approach in terms of stationary scattering theory
Teoretičeskaâ i matematičeskaâ fizika, Tome 98 (1994) no. 2, pp. 248-265

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The Lax–Phillips approach for the Schrödinger equation is reformulated in terms of $t$ and $s$-matrices from stationary scattering theory. New proofs of the incoming and outgoing subspaces orthogonality and analytic continuability of the resolvents on the non-physycal sheet are given. The obtained results are generated to the case of multichannel Hamiltonians for analytic continuation on the non-physical sheet which is connected with the physical one by crossing through the interval between lower thresholds. 
@article{TMF_1994_98_2_a6,
     author = {A. K. Motovilov},
     title = {Reformulation of the {Lax--Phillips} approach in terms of stationary scattering theory},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {248--265},
     publisher = {mathdoc},
     volume = {98},
     number = {2},
     year = {1994},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1994_98_2_a6/}
}
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A. K. Motovilov. Reformulation of the Lax--Phillips approach in terms of stationary scattering theory. Teoretičeskaâ i matematičeskaâ fizika, Tome 98 (1994) no. 2, pp. 248-265. http://geodesic.mathdoc.fr/item/TMF_1994_98_2_a6/