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We give a survey of recent results concerning Schrödinger operators describing the motion of a quantum mechanical particle in ℝ3 or ℝ1 under the influence of a potential concentrated at N centers, N≦∞. We dedicate particular attention to the case N=∞, with centers forming a periodic lattice (model of a crystal) or with centers randomly distributed with random strengths (models of disordered...
We give an expository presentation of the convergence proof for asymptotic observables in N-body quantum systems. Some applications are derived. We use simplifying assumptions and add numerous remarks to stress the main ideas and techniques and to avoid technicalities. Auxiliary concepts like "k-clustered operators" and local decay of subsystems are discussed in detail.
Existence and strong completeness of the wave operators is shown for a new class of one - dimensional Stark effect Hamiltonians using a commutator method.
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