Quantum motion on a half-line connected to a plane

DOI10.1063/1.527670zbMath0634.46057OpenAlexW2015849711MaRDI QIDQ3772749

Pavel Exner, Petr Šeba

Publication date: 1987

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.527670

zbMATH Keywords

scatteringreflection coefficientfree motion of a particle on a manifold that consists of a one- dimensional and a two-dimensional part connected in one pointself- adjoint extensions

Mathematics Subject Classification ID

Linear symmetric and selfadjoint operators (unbounded) (47B25) Dilations, extensions, compressions of linear operators (47A20) Scattering theory of linear operators (47A40) Miscellaneous applications of functional analysis (46N99)

Related Items (13)

Some examples in one-dimensional ``geometric scattering on manifolds ⋮ Ground states for the planar NLSE with a point defect as minimizers of the constrained energy ⋮ The free Dirac operator on compact and noncompact graphs ⋮ A quantum hybrid with a thin antenna at the vertex of a wedge ⋮ Dynamics of an electron confined to a ``hybrid plane and interacting with a magnetic field ⋮ Quantum controllability on graph-like manifolds through magnetic potentials and boundary conditions ⋮ The von Neumann way to treat systems of mixed dimensionality ⋮ Single point interactions, quantization by parts, and boundary conditions ⋮ Approximations by graphs and emergence of global structures ⋮ Behavior of quasi-particles on hybrid spaces. Relations to the geometry of geodesics and to the problems of analytic number theory ⋮ Quantum circuits and Schrödinger's cat states ⋮ A ``hybrid plane with spin-orbit interaction ⋮ Solutions of the wave equation on hybrid spaces of constant curvature

Cites Work

• Tunneling through a singular potential barrier
• Deficiency indices and singular boundary conditions in quantum mechanics

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