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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.
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참고문헌 (14)
참고문헌 신청
S. Agmon / 1975 / Spectral properties of Schrodinger operators and scattering theory / Ann. Scuola Norm. Sup. Pisa Cl. Sci 2(2):151~218
S. Albeverio / 2005 / Solvable models in quantum mechanics, second edition / AMS Chelsea Publishing
Horia D. Cornean / 2019 / Two-dimensional Schrödinger operators with point interactions: Threshold expansions, zero modes and Lp-boundedness of wave operators / Reviews in Mathematical Physics 31(04):1950012
P. A. Deift / 1978 / Applications of a commutation formula / Duke Math. J 45(2):267~310
G. Dell'Antonio / 2018 / Lp-boundedness of wave operators for the three-dimensional multi-centre point interaction / Ann. Henri Poincare 19(1):283~322
S. Albeverio / 2005 / Solvable models in quantum mechanics, second edition / AMS Chelsea Publishing
Horia D. Cornean / 2019 / Two-dimensional Schrödinger operators with point interactions: Threshold expansions, zero modes and Lp-boundedness of wave operators / Reviews in Mathematical Physics 31(04):1950012
P. A. Deift / 1978 / Applications of a commutation formula / Duke Math. J 45(2):267~310
G. Dell'Antonio / 2018 / Lp-boundedness of wave operators for the three-dimensional multi-centre point interaction / Ann. Henri Poincare 19(1):283~322
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