Abstract
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 Schrodinger differential equation it is shown that bound states may exist for an interaction which decays (or grows) sufficiently slowly in time. Bibliography: 20 titles.
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