Geodesic
On the asymptotic behavior of solutions of the time-dependent Schr\"odinger equation
Sbornik. Mathematics, Tome 39 (1981) no. 2, pp. 169-188

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The asymptotics for large time of solutions of an evolution equation with a selfadjoint Hamiltonian $H(t)$ having discrete spectrum are studied. Conditions are found under which the evolution equation has a solution which behaves asymptotically like an eigenfunction of the operator $H(t)$. In application to the Schrödinger differential equation it is shown that “bound states” may exist for an interaction which decays (or grows) sufficiently slowly in time. Bibliography: 20 titles. 
@article{SM_1981_39_2_a1,
     author = {D. R. Yafaev},
     title = {On the asymptotic behavior of solutions of the time-dependent {Schr\"odinger} equation},
     journal = {Sbornik. Mathematics},
     pages = {169--188},
     publisher = {mathdoc},
     volume = {39},
     number = {2},
     year = {1981},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1981_39_2_a1/}
}
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D. R. Yafaev. On the asymptotic behavior of solutions of the time-dependent Schr\"odinger equation. Sbornik. Mathematics, Tome 39 (1981) no. 2, pp. 169-188. http://geodesic.mathdoc.fr/item/SM_1981_39_2_a1/