The Stability of Matter in Quantum Mechanics by Elliott H. Lieb | (PDF) Free Download

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Research into the stability of matter has been one of the most successful chapters in mathematical physics, and is a prime example of how modern mathematics can be applied to problems in physics. A unique account of the subject, this book provides a complete, self-contained description of research on the stability of matter problem. It introduces the necessary quantum mechanics to mathematicians, and aspects of functional analysis to physicists. The topics covered include electrodynamics of classical and quantized fields, Lieb-Thirring and other inequalities in spectral theory, inequalities in electrostatics, stability of large Coulomb systems, gravitational stability of stars, basics of equilibrium statistical mechanics, and the existence of the thermodynamic limit. The book is an up-to-date account for researchers, and its pedagogical style makes it suitable for advanced undergraduate and graduate courses in mathematical physics.

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⭐The problem of the stability of matter was raised at the end of the nineteenth century:To prevent the negatively charged electron from falling onto the positively charged nucleus, the electron was assumed to orbit the nucleus. Thus, the electric attraction between the electron and the proton would be balanced by the centripetal force of the central motion.Since an orbiting electron is accelerating towards the center, the electron would radiate its energy, and spiral onto the nucleus. This raised again the question of the stability of matter. Namely, how does an Atom not collapse in a split second, as Electrodynamics shows that it should.To answer that question, Bohr conjectured that the orbits of the electron around the nucleus are of fixed energy, and momentum. That the electron moved in loss-less energy orbits, so that no spiraling onto the nucleus may occur.Bohr’s conjecture did not explain how these lossless orbits were available: It seemed right to claim that the momentum was quantized in units of h-bar just like the radiation energy was quantized in units of h (h being the Planck constant). And the Conjecture lead to a credible explanation of the Hydrogen Spectrum.Nevertheless, the question of the stability of matter was only reformulated: The electron does not spiral onto the nucleus because it stays in lossless orbits. But how are there lossless electron orbits? because Bohr conjectured so? Because the electron minds that its orbital momentum be quantized?Note that the question of radiation in the orbit was raised by Classical Electrodynamics, and to avoid a contradiction between Electrodynamics and Quantum Mechanics, the answer should come from Electrodynamics.In a recent paper, ([…]) we explained that in the lossless energy orbits, the radiation energy lost by the proton in its (very small) orbit around the center of the motion, compensates for the radiation energy lost by the electron in its orbit around the center of the motion.First, Quantum Mechanics cannot be used to resolve an Electrodynamics problem, without leaving a contradiction between the two theories.Second, the later Quantum Mechanics of Dirac, Heisenberg, and Schrödinger is based on its own postulates. By applying Quantum Mechanics to the problem of the Stability of matter, we are applying postulates that may very well guarantee the stability of matter. We then establish the stability of matter by assuming the stability of matter. A potential logical failure.Third, the book is devoid of physical intuition, and counts on Abstract mathematical analysis, for which the reader is referred to the author’s other book.If you are seeking a credible explanation to the stability of matter, you will not find it in this book.

⭐This so-called review is ragged and from a professional perspective definitely meaningless. Quantum mechanics developed by Heisenberg and others is a theory generalizing classical mechanics and relativistic field theory to the atomic scale. The classical laws of physics do not apply there. They emerge on a larger scale as a limit case. To argue on the basics of not applicable physical laws is hardly a scientific approach. While Heisenberg uncertainty principle explains (not postulates) that atoms do not collaps, it does not explain why we are not a few millimeters tall. Freeman Dyson realized that it was a mathematically well posed and managable task to address this question with the mathematical tools of functional analysis. But it was Elliott Lieb alone or together with a hand full of coworkers who actually did the work in almost all relevant cases and provided these pioneering, ingenious, very accurate and last but not least rigorous results. The authors of this book did a great job in presenting the complicated matter in a coherent and comprehensable way, thereby making it accessable to students and non-specialists. The importance of the original works reviewed here can hardly be overestimated and it is a shame that the Nobel committee ignored them for so long, while awarding in part far less important achievements.

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