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Principle of limiting absorption forN-body Schrödinger operators —A remark on the commutator method

✍ Scribed by H. Tamura

Publisher
Springer
Year
1989
Tongue
English
Weight
224 KB
Volume
17
Category
Article
ISSN
0377-9017

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✦ Synopsis

We consider a N-body SehrOdinger operator H = Ho + V. The interaction V is given by a sum of pair potentials Vjk(y) ( = Vj~, + V~,), y e R 3. We assume that: V~ = O([y[-(l +o)), p > 0, as lyl ~ oo for the short-range part VA; tgyVj~,=O(lYl-{l~l+')), 0~<lal~<l, as lYl~oo for the long-range part Vj~. Under this assumption, we prove the principle of limiting absorption for H. The obtained result is essentially as good as those obtained in the two-body case. The proof is done by a slight modification of the remarkable commutator method due to Mourre.

📜 SIMILAR VOLUMES

A Limiting Absorption Principle for Schr
A Limiting Absorption Principle for Schrödinger Operators with Generalized Von Neumann–Wigner Potentials I. Construction of Approximate Phase
✍ Peter Rejto; Mario Taboada 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 317 KB

In this series of papers we prove the limiting absorption principle over a given interval for a class of Hamiltonians which contains the original one of von Neumann and Wigner. More specifically, the Hamiltonians are of the form < < < < ␤ Ž . Ž . y⌬ q c sin b x r x q V x , where 2r3 -␤ F 1, V x is a