We consider various forms of boundary-value conditions for general one-dimensional Schrödinger operators with point interactions that include $\delta$- and $\delta'$- interactions, $\delta'$- potential, and $\delta$- magnetic potential. We give most simple spectral properties of such operators, and consider a possibility of finding their norm resolvent approximations.
J. F. Brasche and L. P. Nizhnik, One-dimensional Schrödinger operators with general point interactions, Methods Funct. Anal. Topology 19
(2013), no. 1, 4-15.
BibTex
@article {MFAT675,
AUTHOR = {Brasche, J. F. and Nizhnik, L. P.},
TITLE = {One-dimensional Schrödinger operators with general point interactions},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {19},
YEAR = {2013},
NUMBER = {1},
PAGES = {4-15},
ISSN = {1029-3531},
MRNUMBER = {MR3088074},
ZBLNUMBER = {1289.47089},
URL = {http://mfat.imath.kiev.ua/article/?id=675},
}