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Full-Text Articles in Physical Sciences and Mathematics
Stiefel And Grassmann Manifolds In Quantum Chemistry, Eduardo Chiumiento, Michael Melgaard
Stiefel And Grassmann Manifolds In Quantum Chemistry, Eduardo Chiumiento, Michael Melgaard
Articles
We establish geometric properties of Stiefel and Grassmann manifolds which arise in relation to Slatertype variational spaces in many-particle Hartree-Fock theory and beyond. In particular, we prove thatthey are analytic homogeneous spaces and submanifolds of the space of bounded operators on the single-particle Hilbert space. As a by-product we obtain that they are complete Finsler manifolds. These geometric properties underpin state-of-the-art results on existence of solutions to Hartree-Fock type equations.
Abstract Criteria For Multiple Solutions To Nonlinear Coupled Equations Involving Magnetic Schrodinger Operators, Mattias Enstedt, Michael Melgaard
Abstract Criteria For Multiple Solutions To Nonlinear Coupled Equations Involving Magnetic Schrodinger Operators, Mattias Enstedt, Michael Melgaard
Articles
We consider a system of nonlinear coupled equations involving magnetic Schrodinger
operators and general potentials. We provide a criteria for the existence of multiple
solutions to these equations. As special cases we get the classical results on
existence of innitely many distinct solutions within Hartree and Hartree-Fock
theory of atoms and molecules subject to an external magnetic fields. We also
extend recent results within this theory, including Coulomb system with a constant
magnetic field, a decreasing magnetic field and a "physically measurable" magnetic field.