A limiting absorption principle for Schrödinger operators with oscillating potentials. Part II: \(-\Delta+(c\sin b|x|)/|x|+V(x)\) for short range \(V\) and small coupling constant \(c\) (Q760563)
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scientific article; zbMATH DE number 3884510
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A limiting absorption principle for Schrödinger operators with oscillating potentials. Part II: \(-\Delta+(c\sin b|x|)/|x|+V(x)\) for short range \(V\) and small coupling constant \(c\) |
scientific article; zbMATH DE number 3884510 |
Statements
A limiting absorption principle for Schrödinger operators with oscillating potentials. Part II: \(-\Delta+(c\sin b|x|)/|x|+V(x)\) for short range \(V\) and small coupling constant \(c\) (English)
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1983
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This paper is the continuation of Part I [ibid. 49, 29-84 (1983; Zbl 0537.34024)] of a limiting absorption principle for the Schrödinger operator. But here, the discussion corresponds to \(H=-\Delta +(c \sin (b_ e))/\rho +V(x),\rho\) \(=| x|\), \(x\in {\mathbb{R}}^ n\) where V(x) is a short range potential and c a small coupling constant. An important theorem concerning the eigenvalues of H and several lemmas are given. Then the complete proofs are presented.
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Schrödinger operator
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oscillating potential
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limiting absorption principle
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eigenvalues
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0.97673464
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0.9296626
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0.89762086
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0.8961946
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0.89221174
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0.8897905
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