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 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.
Fulltext:
PDF file (1168 kB)
