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J. Korean Math. Soc. 2020; 57(2): 429-450

Online first article July 17, 2019      Printed March 1, 2020

https://doi.org/10.4134/JKMS.j190127

Copyright © The Korean Mathematical Society.

On the approximation by regular potentials of Schr\"odinger operators with point interactions

Artbazar Galtbayar, Kenji Yajima

National University of Mongolia; Gakushuin University

Abstract

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We prove that wave operators for Schr\"odinger operators with multi-center local point interactions are scaling limits of the ones for Schr\"odinger operators with regular potentials. We simultaneously present a proof of the corresponding well known result for the resolvent which substantially simplifies the one by Albeverio et al.

Keywords: Point interactions, selfadjoint extensions, scattering theory, wave operators

MSC numbers: Primary 47A10, 81Q10, 81Uxx

Supported by: The research of A. Galtbayar was partially supported by the grant No. 839 of Mongolian FST, K. Yajima is supported by JSPS grant in aid for scientific research No. 16K05242 and No. 19K03589.

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