Higher order Schrodinger and Hartree-Fock equations

Abstract

The domain of validity of the higher-order Schrodinger equations is analyzed for harmonic-oscillator and Coulomb potentials as typical examples. Then the Cauchy theory for higher-order Hartree-Fock equations with bounded and Coulomb potentials is developed. Finally, the existence of associated ground states for the odd-order equations is proved. This renders these quantum equations relevant for physics.

19 pages, to appear in J. Math. Phys

References in corpus (6)

• Geometric methods for nonlinear many-body quantum systems
• Classical limit for semi-relativistic Hartree systems
• The Spinless Relativistic Woods-Saxon Problem
• Schroedinger secant lower bounds to semirelativistic eigenvalues
• Extended States for Polyharmonic Operators with Quasi-periodic Potentials in Dimension Two
• Semirelativistic Bound-State Equations: Trivial Considerations

Cited by in corpus (3)

• Kato smoothing, Strichartz and uniform Sobolev estimates for fractional operators with sharp Hardy potentials
• Quantum and classical probability distributions for arbitrary Hamiltonian
• The Lieb-Yau Conjecture for Ground States of Pseudo-Relativistic Boson Stars