Point Interactions in a Line and the Riesz Bases of δ-Functions
Sign Up to like & getrecommendations! Published in 2018 at "Ukrainian Mathematical Journal"
DOI: 10.1007/s11253-018-1477-0
Abstract: We present a description of the relationship between the Sobolev spaces W21$$ {W}_2^1 $$(ℝ) and W22$$ {W}_2^2 $$(ℝ) and the Hilbert space ℓ2. Let Y be a finite or countable set of points on ℝ… read more here.
Keywords: riesz bases; point interactions; interactions line; bases functions ... See more keywords
Resonant transmission in one-dimensional quantum mechanics with two independent point interactions: Full parameter analysis
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DOI: 10.1016/j.aop.2017.08.031
Abstract: Abstract We discuss the scattering of a quantum particle by two independent successive point interactions in one dimension. The parameter space for two point interactions is given by U ( 2 ) × U (… read more here.
Keywords: resonant transmission; point interactions; point; parameter ... See more keywords
Random Hamiltonians with arbitrary point interactions in one dimension
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DOI: 10.1016/j.jde.2021.01.044
Abstract: Abstract We consider disordered Hamiltonians given by the Laplace operator subject to arbitrary random self-adjoint singular perturbations supported on random discrete subsets of the real line. Under minimal assumptions on the type of disorder, we… read more here.
Keywords: arbitrary point; point interactions; random hamiltonians; interactions one ... See more keywords