Ground State for the Relativistic One Electron Atom in a Self-Generated Electromagnetic Field

DOI10.1137/18M1222284zbMath1428.35421arXiv1810.09328MaRDI QIDQ5231306

Margherita Nolasco, Vittorio Coti Zelati

Publication date: 26 August 2019

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.09328

zbMATH Keywords

variational methodsground stateDirac-Maxwell

Mathematics Subject Classification ID

Existence of solutions for minimax problems (49J35) PDEs in connection with quantum mechanics (35Q40) Maxwell equations (35Q61) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items (3)

Normalized solutions for the Klein-Gordon-Dirac system ⋮ A new definition of the Dirac-Fock ground state ⋮ A normalized solitary wave solution of the Maxwell-Dirac equations

Cites Work

• A variational approach to the Brown-Ravenhall operator for the relativistic one-electron atoms
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• Stationary solutions of the Maxwell-Dirac and the Klein-Gordon-Dirac equations
• Ground states for pseudo-relativistic Hartree equations of critical type
• On a class of first order Hamilton-Jacobi equations in metric spaces
• Stability of atoms in the Brown-Ravenhall model
• On the minimax principle for Coulomb-Dirac operators
• Variational methods in relativistic quantum mechanics
• A Smooth Variational Principle With Applications to Subdifferentiability and to Differentiability of Convex Functions
• Strict Positivity of a Relativistic Hamiltonian Due to Brown and Ravenhall
• Normalized Solutions to Strongly Indefinite Semilinear Equations
• Layer solutions in a half‐space for boundary reactions

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