Geodesic
``Eigenfunctions'' of~the nonstationary Schr\"odinger equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 43 (1980) no. 2, pp. 228-239

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Two one-dimensional particles are considered with the interaction which is described by means of time-dependent boundary condition in the corresponding Schrödinger equation. The asymptotics of the wave function of this problem at large times is investigated. The existence of states which are similar to bound states for stationary hamiltonians is established. 
@article{TMF_1980_43_2_a5,
     author = {D. R. Yafaev},
     title = {``Eigenfunctions'' of~the nonstationary {Schr\"odinger} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {228--239},
     publisher = {mathdoc},
     volume = {43},
     number = {2},
     year = {1980},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1980_43_2_a5/}
}
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D. R. Yafaev. ``Eigenfunctions'' of~the nonstationary Schr\"odinger equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 43 (1980) no. 2, pp. 228-239. http://geodesic.mathdoc.fr/item/TMF_1980_43_2_a5/