Norm resolvent convergence of singularly scaled Schr\'odinger operators and \delta'-potentials
| Autor: | Golovaty, Yu. D., Hryniv, R. O. |
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| Rok vydání: | 2011 |
| Předmět: | |
| Zdroj: | Proceedings of the Royal Society of Edinburgh, 143A, 791-816, 2013 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1017/S0308210512000194 |
| Popis: | For a real-valued function V from the Faddeev-Marchenko class, we prove the norm resolvent convergence, as \epsilon goes to 0, of a family S_\epsilon of one-dimensional Schr\"odinger operators on the line of the form S_\epsilon:= -D^2 + \epsilon^{-2} V(x/\epsilon). Under certain conditions the family of potentials converges in the sense of distributions to the first derivative of the Dirac delta-function, and then the limit of S_\epsilon might be considered as a "physically motivated" interpretation of the one-dimensional Schr\"odinger operator with potential \delta'. Comment: 30 pages, 2 figure; submitted to Proceedings of the Royal Society of Edinburgh |
| Databáze: | arXiv |
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