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Minimal escape velocities. (English) Zbl 0944.35014
The authors consider the time-dependent Schrödinger operator on \({\mathbb R}^n\) and estimate the long-time behavior of the wavefunction. This is done by using the Mourre inequality [E. Mourre, Commun. Math. Phys. 78, 391-408 (1981; Zbl 0489.47010)] and by exploiting the expectation values of certain observables. Such decay estimates are related to the smoothness of the resolvent of the Schrödinger operator [A. Jensen, É. Mourre and P. Perry, Ann. Inst. Henri Poincaré, Phys. Theor. 41, 207-225 (1984; Zbl 0561.47007)].

MSC:
35J10 Schrödinger operator, Schrödinger equation
47N50 Applications of operator theory in the physical sciences
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