Schrödinger operators with singular magnetic vector potentials

From MaRDI portal

Publication:5904869

Jump to:navigation, search

DOI10.1007/BF01258900zbMath0468.35038MaRDI QIDQ5904869

Herbert Leinfelder, Christian G. Simader

Publication date: 1981

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/183666

zbMATH Keywords

comparison theorem truncation methods essentially self adjoint formal Schrödinger operator singular magnetic vector potentials

Mathematics Subject Classification ID

Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Linear symmetric and selfadjoint operators (unbounded) (47B25) A priori estimates in context of PDEs (35B45) Schrödinger operator, Schrödinger equation (35J10) Other special methods applied to PDEs (35A25)

Related Items (only showing first 100 items - show all)

Twelve tales in mathematical physics: An expanded Heineman prize lecture ⋮ EIGENFUNCTION EXPANSIONS OF THE MAGNETIC SCHRÖDINGER OPERATOR IN BOUNDED DOMAINS. ⋮ The magnetic Weyl calculus ⋮ On estimation of the number of eigenvalues of the magnetic Schrödinger operator in a three-dimensional layer ⋮ The fate of Landau levels under \(\delta\)-interactions ⋮ New critical point theorem and infinitely many small-magnitude solutions of a nonlinear Iwatsuka model ⋮ Self‐adjointness of non‐semibounded covariant Schrödinger operators on Riemannian manifolds ⋮ Ultra-generalized Wannier bases: Are they relevant to topological transport? ⋮ Quantum systems at the brink: existence of bound states, critical potentials, and dimensionality ⋮ Derivation of the Dipolar Gross--Pitaevskii Energy ⋮ Estimates on modulation spaces for Schrödinger operators with time-dependent sub-linear vector potentials ⋮ A geometric Iwatsuka type effect in quantum layers ⋮ Unitary propagators for N-body Schrödinger equations in external field ⋮ Heat kernel asymptotics for magnetic Schrödinger operators ⋮ Time-periodic oscillations in suspension bridges: Existence of unique solutions ⋮ On moments of negative eigenvalues for the Pauli operator ⋮ On the maximal ionization for the atomic Pauli operator ⋮ Essential self-adjointness for semi-bounded magnetic Schrödinger operators on non-compact manifolds ⋮ Eigenvalue asymptotics for the södinger operator ⋮ Exponential decay estimates for fundamental solutions of Schrödinger-type operators ⋮ On moments of negative eigenvalues for the Pauli operator ⋮ Product Formula for Resolvents of Normal Operators and the Modified Feynman Integral ⋮ Tosio Kato’s work on non-relativistic quantum mechanics, Part 2 ⋮ The Liouville equation for singular ergodic magnetic Schrödinger operators ⋮ Averaging of magnetic fields and applications ⋮ Moment analysis for localization in random Schrödinger operators ⋮ CONTINUITY PROPERTIES OF SCHRÖDINGER SEMIGROUPS WITH MAGNETIC FIELDS ⋮ Essential self-adjointness of second-order elliptic operator with measurable coefficients ⋮ Discreteness of Spectrum and Strict Positivity Criteria for Magnetic Schrödinger Operators ⋮ Feynman-Kac formulas for Dirichlet-Pauli-Fierz operators with singular coefficients ⋮ On the number of negative eigenvalues for a Schrödinger operator with magnetic field ⋮ Asymptotic \(\hslash^{1/2}\)-expansions in classic particle limit of non- relativistic quantum mechanics ⋮ Estimates on modulation spaces for Schrödinger operators with first order magnetic fields ⋮ Examples of absolutely continuous Schrödinger operators in magnetic fields ⋮ Absorption semigroups, their generators, and Schrödinger semigroups ⋮ Regularization of atomic Schrödinger operators with magnetic field ⋮ Quantum magnetic billiards: boundary conditions and gauge transformations ⋮ DISCRETENESS OF SPECTRUM FOR THE MAGNETIC SCHRÖDINGER OPERATORS ⋮ PATH INTEGRAL REPRESENTATION FOR SCHRÖDINGER OPERATORS WITH BERNSTEIN FUNCTIONS OF THE LAPLACIAN ⋮ Wegner estimates, Lifshitz tails, and Anderson localization for Gaussian random magnetic fields ⋮ Scattering in the energy space for the NLS with variable coefficients ⋮ Optimal heat kernel estimates for Schrödinger operators with magnetic fields in two dimensions ⋮ Estimate of the difference between the Kac operator and the Schrödinger semigroup ⋮ Existence and completeness of the wave operators for higher order differential operators ⋮ Limiting absorption principle for schrödinger hamiltonians with magnetic fields ⋮ Pauli-Fierz type operators with singular electromagnetic potentials on general domains ⋮ Schrödinger equations with time-dependent strong magnetic fields ⋮ Strichartz estimates for the magnetic Schrödinger equation ⋮ On the discreteness of the spectrum of the magnetic Schrödinger operator ⋮ Nonlinear Schrödinger equations with steep magnetic well ⋮ The geometry of (non-abelian) Landau levels ⋮ Nonselfadjoint Schrödinger operators with singular first-order coefficients ⋮ The forward problem for the electromagnetic Helmholtz equation with critical singularities ⋮ Notes on the Cauchy problem for the self-adjoint and non-self-adjoint Schrödinger equations with polynomially growing potentials ⋮ Singular first order perturbations of the heat equation ⋮ The \(m\)-accretivity of covariant Schrödinger operators with unbounded drift ⋮ Impenetrability of Aharonov-Bohm solenoids: proof of norm resolvent convergence ⋮ A rigorous mathematical construction of Feynman path integrals for the Schrödinger equation with magnetic field ⋮ Schrödinger operators with magnetic and electric potentials ⋮ Radiation conditions for the magnetic Helmholtz equation ⋮ The continuity and the differentiability of solutions on parameters to the Schrödinger equations and the Dirac equations ⋮ ``Localized self-adjointness of Schrödinger type operators on Riemannian manifolds. ⋮ Dirichlet forms for singular one-dimensional operators and on graphs ⋮ Localization of generalized Wannier bases implies Chern triviality in non-periodic insulators ⋮ Normal forms of an abstract Dirac operator and applications to scattering theory ⋮ Laplacian cut-offs, porous and fast diffusion on manifolds and other applications ⋮ ON THE STRONG UNIQUENESS OF SOME FINITE DIMENSIONAL DIRICHLET OPERATORS ⋮ An elementary proof of Harnack's inequality for Schrödinger operators and related topics ⋮ Quantization of edge currents along magnetic barriers and magnetic guides ⋮ Abstract criteria for multiple solutions to nonlinear coupled equations involving magnetic Schrödinger operators ⋮ Surface Lifshits tails for random quantum Hamiltonians ⋮ Eigenvalue asymptotics for the Schrödinger operator with steplike magnetic field and slowly decreasing electric potential ⋮ Essential selfadjointness of singular magnetic Schrödinger operators on Riemannian manifolds ⋮ On bounds of \(N(\lambda)\) for a magnetic Schrödinger operator ⋮ Lp estimates for parabolic magnetic Schrödinger operators ⋮ \(L^{p}\)-interpolation inequalities and global Sobolev regularity results (with an appendix by Ognjen Milatović) ⋮ A new critical point theorem and small magnitude solutions of magnetic Schrödinger equations with Landau levels ⋮ Existence of a solution to Hartree-Fock equations with decreasing magnetic fields ⋮ Schrödinger operators in the twentieth century ⋮ Tosio Kato's work on non-relativistic quantum mechanics. I ⋮ Eigenvalues of the Klein-Gordon equation ⋮ Border-line eigenvalue asymptotics for the Schrödinger operator with electromagnetic potential ⋮ Polynomial boundedness of eigensolutions and the spectrum of Schrödinger operators ⋮ Wegner estimate and localization for random magnetic fields ⋮ Note on the kinetic energy inequality leading to Lieb's negative ionization upper bound ⋮ Schrödinger operators with random \(\delta \) magnetic fields ⋮ The essential spectrum of Schrödinger, Jacobi, and CMV operators ⋮ An evolution equation approach to the Klein-Gordon operator on curved spacetime ⋮ Eigenvalue asymptotics and exponential decay of eigenfunctions for Schrödinger operators with magnetic fields ⋮ Energy concentration and explicit Sommerfeld radiation condition for the electromagnetic Helmholtz equation ⋮ New bounds on the maximum ionization of atoms ⋮ Comparaison des semi-groupes associes a des operateurs de schrödinger dans un champ mangetique ⋮ Endpoint Strichartz estimates for the magnetic Schrödinger equation ⋮ Schrödinger semigroups ⋮ An infinite-temperature limit for a quantum scattering process ⋮ Coherent electronic transport in periodic crystals ⋮ Non-existence of a minimizer to the magnetic Hartree-Fock functional ⋮ Unnamed Item ⋮ Abstract theory of pointwise decay with applications to wave and Schrödinger equations ⋮ Magnetic virial identities, weak dispersion and Strichartz inequalities

Cites Work

This page was built for publication: Schrödinger operators with singular magnetic vector potentials

Retrieved from "https://portal.mardi4nfdi.de/w/index.php?title=Publication:5904869&oldid=13219911"