Self-adjoint extension schemes and modern applications to quantum Hamiltonians
M Gallone, A Michelangeli, S Albeverio - 2023 - Springer
This book introduces and discusses the self-adjoint extension problem for symmetric
operators on Hilbert space. It presents the classical von Neumann and Krein–Vishik–Birman …
operators on Hilbert space. It presents the classical von Neumann and Krein–Vishik–Birman …
Essential self-adjointness for combinatorial Schrödinger operators II-Metrically non complete graphs
Y Colin de Verdière, N Torki-Hamza, F Truc - … Physics, Analysis and …, 2011 - Springer
Essential Self-adjointness for Combinatorial Schrödinger Operators II-Metrically non Complete
Graphs Page 1 Math Phys Anal Geom (2011) 14:21–38 DOI 10.1007/s11040-010-9086-7 …
Graphs Page 1 Math Phys Anal Geom (2011) 14:21–38 DOI 10.1007/s11040-010-9086-7 …
Quantum confinement on non-complete Riemannian manifolds
We consider the quantum completeness problem, ie the problem of confining quantum
particles, on a non-complete Riemannian manifold M equipped with a smooth measure …
particles, on a non-complete Riemannian manifold M equipped with a smooth measure …
On the essential self-adjointness of singular sub-Laplacians
We prove a general essential self-adjointness criterion for sub-Laplacians on complete sub-
Riemannian manifolds, defined with respect to singular measures. We also show that, in the …
Riemannian manifolds, defined with respect to singular measures. We also show that, in the …
Essential self-adjointness for combinatorial Schrödinger operators III-Magnetic fields
Y Colin de Verdière, N Torki-Hamza… - Annales de la Faculté des …, 2011 - numdam.org
We define the magnetic Schrödinger operator on an infinite graph by the data of a magnetic
field, some weights on vertices and some weights on edges. We discuss essential self …
field, some weights on vertices and some weights on edges. We discuss essential self …
Laplaciens de graphes infinis I-Graphes métriquement complets
N Torki-Hamza - Confluentes Mathematici, 2010 - World Scientific
We introduce the weighted graph Laplacian Δω, c and the notion of Schrödinger operator of
the form Δ1, a+ W on a locally finite graph G. Concerning essential self-adjointness, we …
the form Δ1, a+ W on a locally finite graph G. Concerning essential self-adjointness, we …
On the existence and uniqueness of self-adjoint realizations of discrete (magnetic) Schrödinger operators
M Schmidt - Analysis and geometry on graphs and manifolds, 2020 - books.google.com
In this expository chapter we answer two fundamental questions concerning discrete
magnetic Schrödinger operator associated with weighted graphs. We discuss when formal …
magnetic Schrödinger operator associated with weighted graphs. We discuss when formal …
On geometric quantum confinement in Grushin-type manifolds
We study the problem of so-called geometric quantum confinement in a class of two-
dimensional incomplete Riemannian manifold with metric of Grushin type. We employ a …
dimensional incomplete Riemannian manifold with metric of Grushin type. We employ a …
Confining quantum particles with a purely magnetic field
Y Colin de Verdière, F Truc - Annales de l'institut Fourier, 2010 - numdam.org
Let us consider a particle in a domain Ω in Rd (d⩾ 2) in the presence of a magnetic field B.
We will always assume that the topological boundary∂ Ω:= Ω Ω of Ω is compact. At the …
We will always assume that the topological boundary∂ Ω:= Ω Ω of Ω is compact. At the …