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

Citations:

Zbl 0489.47010; Zbl 0561.47007
Full Text:

References:

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