Differential Equations of Quantum Mechanics
arXiv:2208.03774 · doi:10.1090/qam/1611
Abstract
We review very briefly the main mathematical structures and results in some important areas of Quantum Mechanics involving PDEs and formulate open problems.
References in corpus (20)
- Solitary Wave Dynamics in an External Potential
- Fast soliton scattering by delta impurities
- The Electronic Ground State Energy Problem: a New Reduced Density Matrix Approach
- Geometric methods for nonlinear many-body quantum systems
- Semilinear wave equations on the Schwarzschild manifold I: Local decay estimates
- Scattering and small data completeness for the critical nonlinear Schroediger equation
- The BCS Functional for General Pair Interactions
- The time-dependent Born-Oppenheimer approximation
- Absence of Ground States for a Class of Translation Invariant Models of Non-relativistic QED
- Thomas-Fermi approximation for coexisting two component Bose-Einstein condensates and nonexistence of vortices for small rotation
- Ground State and Resonances in the Standard Model of Non-relativistic QED
- Existence of Hartree-Fock excited states for atoms and molecules
- The translation Invariant Massive Nelson Model: II. The Continuous Spectrum Below the Two-boson Threshold
- Coherent infrared representations in non-relativistic QED
- Mass Renormalization and Energy Level Shift in Non-Relativistic QED
- A survey on asymptotic stability of ground states of nonlinear Schrodinger equations II
- The Mass Shell of the Nelson Model without Cut-Offs
- Growth of Sobolev norms in linear Schrödinger equations as a dispersive phenomenon
- Molecular dynamics at an energy-level crossing
- Van der Waals interactions between two hydrogen atoms: The next orders