Schrdinger-operators with singular interactions

JF Brasche Pavel Exner Yu A Kuperin P Seba

TBD mathscidoc:1910.43025

Journal of mathematical analysis and applications, 184, (1), 112-139, 1994.5
Schrodinger operators with strongly singular interactions, typically supported by a set of Lebesgue measure zero, eg, by a nite or countable set of points, appeared in quantum mechanics from the very beginning~cf., eg,[35, 28]. Their use had essentially two motivations. First of all, they were expected to provide a reasonable description in the physical situations when the real interaction has a very small range comparing to the other characteristic lengths of the problem, for instance, to the wavelength of the scattered particles. On the other hand, the fact that the interaction support is small and outside it a free solution of the corresponding Schrodinger equation may be used often makes such models explicitly solvable. Until the beginning of the sixties, however, the occasional use of these point interactions remained purely formal. Only after the work of Berezin and Faddeev [11] did it become clear they can be
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  title={Schrdinger-operators with singular interactions},
  author={JF Brasche, Pavel Exner, Yu A Kuperin, and P Seba},
  booktitle={Journal of mathematical analysis and applications},
JF Brasche, Pavel Exner, Yu A Kuperin, and P Seba. Schrdinger-operators with singular interactions. 1994. Vol. 184. In Journal of mathematical analysis and applications. pp.112-139.
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