ISSN:
1573-0530
Keywords:
35P
;
81F
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Abstract We consider a N-body Schrödinger operator H=H 0+V. The interaction V is given by a sum of pair potentials V jk(y)(=V jk s +V jk l ), y ∈ R3. We assume that: V jk s =O(|y|-(1+p)), p〉0, as |y| → ∞ for the short-range part V jk s ; $$\partial _y^\alpha V_{jk}^l = 0(|y|^{ - (|\alpha | + p)} ),{\text{ }}0 \leqslant {\text{ }}|a| \leqslant 1,{\text{ }}as |y| \to \infty $$ for the long-range part V jk l . 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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00420011
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