Stability and control of a 1D quantum system with confining time dependent delta potentials

Details Stability and control of a 1D quantum system with confining time dependent delta potentials Stability and control of a 1D quantum system with confining time dependent delta potentials

2010-06-16

arxiv.org/abs/1006.3329v3

Mathematics

Analysis of PDEs

latex, 21 pages, title changed

Scientific paper

The evolution problem for a quantum particle confined in a 1D box and interacting with one fixed point through a time dependent point interaction is considered. Under suitable assumptions of regularity for the time profile of the Hamiltonian, we prove the existence of strict solutions to the corresponding Schr\"odinger equation. The result is used to discuss the stability and the steady-state local controllability of the wavefunction when the strenght of the interaction is used as a control parameter.

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