DISCRETE SPECTRUM ASYMPTOTICS FOR THE SCHRÖDINGER OPERATOR WITH A SINGULAR POTENTIAL AND A MAGNETIC FIELD

DOI10.1142/S0129055X96000305zbMath0872.35075OpenAlexW2040509155MaRDI QIDQ4335498

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Publication date: 15 October 1997

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

Full work available at URL: https://doi.org/10.1142/s0129055x96000305

zbMATH Keywords

semiclassical asymptoticssingular potentialtrace asymptotics

Mathematics Subject Classification ID

Asymptotic distributions of eigenvalues in context of PDEs (35P20) Schrödinger operator, Schrödinger equation (35J10)

Related Items (10)

Stability and semiclassics in self-generated fields ⋮ Sharp Weyl laws with singular potentials ⋮ Sharp pointwise Weyl laws for Schrödinger operators with singular potentials on flat tori ⋮ The Scott conjecture for large Coulomb systems: a review ⋮ Second order semiclassics with self-generated magnetic fields ⋮ Scott correction for large atoms and molecules in a self-generated magnetic field ⋮ SEMICLASSICS OF THE QUANTUM CURRENT IN A STRONG CONSTANT MAGNETIC FIELD ⋮ Relativistic Scott correction for atoms and molecules ⋮ Pointwise Weyl laws for Schrödinger operators with singular potentials ⋮ A proof of Scott's correction for matter

Cites Work

• Weak type estimates for singular values and the number of bound states of Schrödinger operators
• Schrödinger operators with magnetic fields. I: General interactions
• Asymptotics of the ground state energies of large Coulomb systems
• Asymptotics of heavy atoms in high magnetic fields. II: Semiclassical regions
• The quasi-classical asymptotics of local Riesz means for the Schrödinger operator in a strong homogeneous magnetic field

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