Higher order Schrodinger and Hartree-Fock equations
Remi Carles (IMAG), Wolfgang Lucha, Emmanuel Moulay (XLIM)
TL;DR
This paper investigates the validity, mathematical foundations, and ground state existence of higher-order Schrödinger and Hartree-Fock equations, extending quantum theory applications.
Contribution
It develops the Cauchy theory for higher-order Hartree-Fock equations and proves the existence of ground states for odd-order cases.
Findings
Validity domains for higher-order Schrödinger equations analyzed
Cauchy theory established for higher-order Hartree-Fock equations
Existence of ground states proved for odd-order 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.
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