Optimal limiting absorption principle for a Schrödinger type operator on a Lipschitz cylinder
✍ Scribed by Michael Melgaard
- Book ID
- 105923479
- Publisher
- Springer
- Year
- 2005
- Tongue
- English
- Weight
- 219 KB
- Volume
- 118
- Category
- Article
- ISSN
- 0025-2611
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📜 SIMILAR VOLUMES
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~.
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
Let H=&2+V be a Schro dinger operator acting in L 2 (S), with S the twodimensional unit sphere, 2 the spherical Laplacian, and V a continuous potential. As is well known, the eigenvalues of H in the l th cluster, i.e., those eigenvalues within a radius sup |V| of l(l+1), the l th eigenvalue of &2, h