Spectral properties of Schrödinger operators and time-decay of the wave functions. Results in \(L^ 2(R^ 4)\). (English) Zbl 0564.35024
The author considers Schrödinger operators \(H=-\Delta +V\) in \(L^ 2({\mathbb{R}}^ 4)\), where \(V(x)=O(| x|^{-\beta})\) as \(| x| \to \infty\) for some \(\beta >0\). Furthermore some local singularities are permitted. He is concerned with the spectral properties of H in the low energy limit. The results are expressed in terms of asymptotic expansions for the resolvent \(R(\zeta)=(H-\zeta)^{-1}\) as \(\zeta\) \(\to 0\).
Reviewer: N.Jacob
MSC:
| 35J10 | Schrödinger operator, Schrödinger equation |
| 35Q99 | Partial differential equations of mathematical physics and other areas of application |
| 35P05 | General topics in linear spectral theory for PDEs |
| 81Q10 | Selfadjoint operator theory in quantum theory, including spectral analysis |
Keywords:
Schrödinger operators; local singularities; spectral properties; low energy limit; asymptotic expansions; resolventReferences:
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