Pointwise bounds for Schrödinger eigenstates

DOI10.1007/BF01248665zbMath0403.47016OpenAlexW2068203379MaRDI QIDQ1256190

René A. Carmona

Publication date: 1978

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

Full work available at URL: https://doi.org/10.1007/bf01248665

Mathematics Subject Classification ID

Spectral theory and eigenvalue problems for partial differential equations (35P99) General theory of partial differential operators (47F05) Schrödinger operator, Schrödinger equation (35J10) (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces (47A70)

Related Items

Twelve tales in mathematical physics: An expanded Heineman prize lecture ⋮ LOCALIZATION OF THE NUMBER OF PHOTONS OF GROUND STATES IN NONRELATIVISTIC QED ⋮ Exponential integrability and exit times of diffusions on sub-Riemannian and metric measure spaces ⋮ Regularity properties of Schrödinger and Dirichlet semigroups ⋮ Brownian motion, \(L^p\) properties of Schrödinger operators and the localization of binding ⋮ Unnamed Item ⋮ An Agmon estimate for Schrödinger operators on graphs ⋮ Probabilistic representation and fall-off of bound states of relativistic Schrödinger operators with spin 1/2 ⋮ Pointwise bounds on eigenfunctions and wave packets in N-body quantum systems. V: Lower bounds and path integrals ⋮ Localization of quantum states and landscape functions ⋮ Gibbs measures on Brownian currents ⋮ Fall-off of eigenfunctions for non-local Schrödinger operators with decaying potentials ⋮ Schrödinger semigroups ⋮ GROUND STATE PROPERTIES OF THE NELSON HAMILTONIAN: A GIBBS MEASURE-BASED APPROACH ⋮ PAULI–FIERZ MODEL WITH KATO-CLASS POTENTIALS AND EXPONENTIAL DECAYS ⋮ On the quantum Feynman-Kac formula ⋮ Relativistic Schrödinger operators: Asymptotic behavior of the eigenfunctions ⋮ GIBBS MEASURES WITH DOUBLE STOCHASTIC INTEGRALS ON A PATH SPACE ⋮ Certain Liouville properties of eigenfunctions of elliptic operators ⋮ Ultracontractivity and the heat kernel for Schrödinger operators and Dirichlet Laplacians ⋮ Pointwise eigenfunction estimates and intrinsic ultracontractivity-type properties of Feynman-Kac semigroups for a class of Lévy processes

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Regularity properties of Schrödinger and Dirichlet semigroups
• A path space picture for Feynman-Kac averages
• Degenerate and non-degenerate ground states for Schrödinger operators
• On the decoupling of finite singularities from the question of asymptotic completeness in two body quantum systems
• Potentials on abstract Wiener space
• Critère de convergence des fonctionnelles de Kac et application en mécanique quantique et en géométrie
• Hypercontractivity for anharmonic oscillators
• Pointwise Bounds on Eigenfunctions and Wave Packets in N-Body Quantum Systems. II
• Pointwise Bounds on Eigenfunctions and Wave Packets in N-Body Quantum Systems. III
• Logarithmic Sobolev Inequalities
• Bounds on the eigenvalues of the Laplace and Schroedinger operators
• Sobolev Inequalities for Weight Spaces and Supercontractivity
• −Δ plus a bad potential
• The Wiener integral and perturbation theory of the Schrödinger operator
• On the Schrodinger and Heat Equations for Nonnegative Potentials
• On Spectra of Second-Order Differential Operators

This page was built for publication: Pointwise bounds for Schrödinger eigenstates