L2 ANALYSIS OF THE MULTI-CONFIGURATION TIME-DEPENDENT HARTREE–FOCK EQUATIONS

DOI10.1142/S0218202510004842zbMath1206.35229arXiv1002.1816MaRDI QIDQ3067105

Norbert J. Mauser, Saber Trabelsi

Publication date: 20 January 2011

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1002.1816

zbMATH Keywords

regularityexistenceStrichartz estimatesmulti-configuration methodsHartree-Fock equations

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Other elementary particle theory in quantum theory (81V25) A priori estimates in context of PDEs (35B45) NLS equations (nonlinear Schrödinger equations) (35Q55) PDEs in connection with quantum mechanics (35Q40) Time-dependent Schrödinger equations and Dirac equations (35Q41) PDEs in connection with mechanics of particles and systems of particles (35Q70)

Related Items (4)

One particle equations for many particle quantum systems: The MCTHDF method ⋮ Dual dynamically orthogonal approximation of incompressible Navier Stokes equations with random boundary conditions ⋮ Symplectic dynamical low rank approximation of wave equations with random parameters ⋮ Setting and analysis of the multi-configuration time-dependent Hartree-Fock equations

Cites Work

• Setting and analysis of the multi-configuration time-dependent Hartree-Fock equations
• Global-in-time existence of solutions to the multiconfiguration time-dependent Hartree-Fock equations: a sufficient condition
• Existence of solutions for Schrödinger evolution equations
• Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations
• Mean field dynamics of fermions and the time-dependent Hartree-Fock equation
• The multiconfiguration equations for atoms and molecules: charge quantization and existence of solutions
• Solutions of the multiconfiguration equations in quantum chemistry
• Solutions of the multiconfiguration time-dependent Hartree-Fock equations with Coulomb interactions
• Global existence of solutions to the Cauchy problem for time-dependent Hartree equations
• L² Solutions to the Schrödinger–Poisson System: Existence, Uniqueness, Time Behaviour, and Smoothing Effects
• Regularity of the multi-configuration time-dependent Hartree approximation in quantum molecular dynamics

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