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Mathematical Physics

arXiv:1805.03063 (math-ph)
[Submitted on 8 May 2018]

Title:Methods of modern mathematical physics: Uncertainty and exclusion principles in quantum mechanics

Authors:Douglas Lundholm
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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.
Comments: 108 pages, 2 figures. Some sections still incomplete
Subjects: Mathematical Physics (math-ph); Functional Analysis (math.FA); Spectral Theory (math.SP)
MSC classes: 81Q10 (Primary) 35P15, 46N50, 81V70 (Secondary)
Cite as: arXiv:1805.03063 [math-ph]
  (or arXiv:1805.03063v1 [math-ph] for this version)
  https://doi.org/10.48550/arXiv.1805.03063

Submission history

From: Douglas Lundholm [view email]
[v1] Tue, 8 May 2018 14:42:40 UTC (114 KB)
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