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A stationary approach to the existence and completeness of long-range wave operators

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Abstract

The modified wave operators intertwining the Schrödinger operators − Δ and − Δ + V(x), where V(x) is a real long-range potential, are shown to exist and to be complete. The method employed is entirely stationary (time-independent) : One constructs complete stationary wave operators, utilizing a spectral representation (eigenfunction expansion) theory, and then shows that the time-dependent modified wave operators exist and are equal to the stationary ones already constructed.

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Authors and Affiliations

  1. Department of Mathematics, Kyoto Uiversity, 606, Kyoto, Japan

    Teruo Ikebe & Hiroshi Isozaki

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  1. Teruo Ikebe
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  2. Hiroshi Isozaki
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Ikebe, T., Isozaki, H. A stationary approach to the existence and completeness of long-range wave operators. Integr equ oper theory 5, 18–49 (1982). https://doi.org/10.1007/BF01694028

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  • DOI: https://doi.org/10.1007/BF01694028

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