A new proof of the analyticity of the electronic density of molecules

DOI10.1007/s11005-010-0401-9zbMath1197.35087arXiv0904.0221OpenAlexW3098783927MaRDI QIDQ5962039

Thierry Jecko

Publication date: 16 September 2010

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

Full work available at URL: https://arxiv.org/abs/0904.0221

zbMATH Keywords

Coulomb potentialanalytic elliptic regularityelectronic densityelliptic regularitymolecular Hamiltonian

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with quantum mechanics (35Q40) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Schrödinger operator, Schrödinger equation (35J10) Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs (35A27) Molecular physics (81V55)

Related Items (11)

On factorization of molecular wavefunctions ⋮ On the analyticity of electronic reduced densities for molecules ⋮ Regularity for eigenfunctions of Schrödinger operators ⋮ The diagonal behaviour of the one-particle Coulombic density matrix ⋮ A regularity result for the bound states of \(N\)-body Schrödinger operators: blow-ups and Lie manifolds ⋮ Tosio Kato's work on non-relativistic quantum mechanics. I ⋮ On the mathematical treatment of the Born-Oppenheimer approximation ⋮ Hohenberg-Kohn theorems for interactions, spin and temperature ⋮ Estimates on derivatives of coulombic wave functions and their electron densities ⋮ Tosio Kato’s work on non-relativistic quantum mechanics, Part 2 ⋮ Analyticity of the one-particle density matrix

Cites Work

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• On the Born-Oppenheimer expansion for polyatomic molecules
• Perturbation theory for linear operators.
• Exponential bounds and absence of positive eigenvalues for N-body Schrödinger operators
• The electron density is smooth away from Nuclei
• Analyticity of the density of electronic wavefunctions
• Non-isotropic cusp conditions and regularity of the electron density of molecules at the nuclei
• Twisted pseudodifferential calculus and application to the quantum evolution of molecules

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