Methods of modern mathematical physics: Uncertainty and exclusion principles in quantum mechanics
arXiv:1805.03063
Abstract
These are lecture notes for a master-level course given at KTH, Stockholm, in the spring of 2017, with the primary aim of proving the stability of matter from first principles using modern mathematical methods in many-body quantum mechanics. General quantitative formulations of the uncertainty and the exclusion principles of quantum mechanics are introduced, such as the Hardy, Sobolev and Poincaré functional inequalities as well as the powerful Lieb-Thirring inequality that combines these two principles. The notes are aimed to be both fairly self-contained and at the same time complementary to existing literature, also covering recent developments to prove Lieb-Thirring inequalities and stability from general, weaker formulations of the exclusion principle.
108 pages, 2 figures. Some sections still incomplete
References in corpus (7)
- Mean-field limit of Bose systems: rigorous results
- Many-anyon trial states
- Exclusion bounds for extended anyons
- Lieb-Thirring inequality with semiclassical constant and gradient error term
- On the Geometry of Supersymmetric Quantum Mechanical Systems
- Partial Hamiltonian reduction of relativistic extended objects in light-cone gauge
- Hamiltonians for Two-Anyon Systems