Higher-order Schrödinger and Hartree–Fock equations

Journal Article · Tue Dec 15 00:00:00 EST 2015 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4936646· OSTI ID:22479569

Carles, Rémi ^[1]; Lucha, Wolfgang ^[2]; Moulay, Emmanuel ^[3]

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1. IMAG, UMR5149, CNRS and University Montpellier, CC051, 34095 Montpellier (France)
2. Institute for High Energy Physics, Austrian Academy of Sciences, Nikolsdorfergasse 18, A-1050 Vienna (Austria)
3. XLIM (UMR-CNRS 7252), University Poitiers, 11 Blvd. Marie et Pierre Curie, BP 30179, 86962 Futuroscope Chasseneuil Cedex (France)

The domain of validity of the higher-order Schrödinger 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.

• OSTI ID: 22479569
• Journal Information: Journal of Mathematical Physics, Vol. 56, Issue 12; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
COULOMB FIELD
GROUND STATES
HARMONIC OSCILLATORS
SCHROEDINGER EQUATION