Tag: dinger

Free Download David Damanik, "One-Dimensional Ergodic Schrödinger Operators "
English | ISBN: 1470470861 | 2022 | 444 pages | PDF | 4 MB
The theory of one-dimensional ergodic operators involves a beautiful synthesis of ideas from dynamical systems, topology, and analysis. Additionally, this setting includes many models of physical interest, including those operators that model crystals, disordered media, or quasicrystals. This field has seen substantial progress in recent decades, much of which has yet to be discussed in textbooks. Beginning with a refresher on key topics in spectral theory, this volume presents the basic theory of discrete one-dimensional Schrödinger operators with dynamically defined potentials. It also includes a self-contained introduction to the relevant aspects of ergodic theory and topological dynamics. This text is accessible to graduate students who have completed one-semester courses in measure theory and complex analysis. It is intended to serve as an introduction to the field for junior researchers and beginning graduate students as well as a reference text for people already working in this area. It is well suited for self-study and contains numerous exercises (many with hints).

Free Download Schrödinger’s Philosophy of Quantum Mechanics By Michel Bitbol (auth.)
1996 | 292 Pages | ISBN: 9401072914 | PDF | 12 MB
This book is the final outcome of two projects. My first project was to publish a set of texts written by Schrodinger at the beginning of the 1950’s for his seminars and lectures at the Dublin Institute for Advanced Studies. These almost completely forgotten texts contained important insights into the interpretation of quantum mechanics, and they provided several ideas which were missing or elusively expressed in SchrOdinger’s published papers and books of the same period. However, they were likely to be misinterpreted out of their context. The problem was that current scholarship could not help very much the reader of these writings to figure out their significance. The few available studies about SchrOdinger’s interpretation of quantum mechanics are generally excellent, but almost entirely restricted to the initial period 1925-1927. Very little work has been done on Schrodinger’s late views on the theory he contributed to create and develop. The generally accepted view is that he never really recovered from his interpretative failure of 1926-1927, and that his late reflections (during the 1950’s) are little more than an expression of his rising nostalgia for the lost ideal of picturing the world, not to say for some favourite traditional picture. But the content and style of Schrodinger’s texts of the 1950’s do not agree at all with this melancholic appraisal; they rather set the stage for a thorough renewal of accepted representations. In order to elucidate this paradox, I adopted several strategies.

Free Download The Nonlinear Schrödinger Equation: Self-Focusing and Wave Collapse by Catherine Sulem, Pirre-Louis Sulem
English | PDF | 1999 | 363 Pages | ISBN : 0387986111 | 3.2 MB
Filling the gap between the mathematical literature and applications to domains, the authors have chosen to address the problem of wave collapse by several methods ranging from rigorous mathematical analysis to formal aymptotic expansions and numerical simulations.

Free Download Spectral Analysis of N-Body Schrödinger Operators at Two-Cluster Thresholds by Erik Skibsted , Xue Ping Wang
English | PDF EPUB (True) | 2024 | 262 Pages | ISBN : 9819726239 | 33.3 MB
This book provides a systematic study of spectral and scattering theory for many-body Schrödinger operators at two-cluster thresholds. While the two-body problem (reduced after separation of the centre of mass motion to a one-body problem at zero energy) is a well-studied subject, the literature on many-body threshold problems is sparse. However, the authors’ analysis covers for example the system of three particles interacting by Coulomb potentials and restricted to a small energy region to the right of a fixed nonzero two-body eigenvalue. In general, the authors address the question: How do scattering quantities for the many-body atomic and molecular models behave within the limit when the total energy approaches a fixed two-cluster threshold? This includes mapping properties and singularities of the limiting scattering matrix, asymptotics of the total scattering cross section, and absence of transmission from one channel to another in the small inter-cluster kinetic energy region. The authors’ principal tools are the Feshbach-Grushin dimension reduction method and spectral analysis based on a certain Mourre estimate. Additional topics of independent interest are the limiting absorption principle, micro-local resolvent estimates, Rellich- and Sommerfeld-type theorems and asymptotics of the limiting resolvents at thresholds. The mathematical physics field under study is very rich, and there are many open problems, several of them stated explicitly in the book for the interested reader.

Free Download From Aristotle to Schrödinger: The Curiosity of Physics by Antonis Modinos
English | PDF (True) | 2014 | 521 Pages | ISBN : 3319007491 | 7.9 MB
From Aristotle to Schrödinger: The Curiosity of Physics offers a novel introduction to the topics commonly encountered in the first two years of an undergraduate physics course, including classical mechanics, thermodynamics and statistical mechanics, electromagnetism, relativity, quantum mechanics, atomic and molecular physics, and astrophysics. The book presents physics as it evolved historically; it covers in considerable depth the development of the subject from ancient Greece to the present day. Though the emphasis is on the observations, experiments, theories, and applications of physics, there are additionally short sections on the life and times of the main protagonists of physics.

Free Download Schrödinger Equations in Nonlinear Systems by Wu-Ming Liu , Emmanuel Kengne
English | PDF (True) | 2019 | 576 Pages | ISBN : 9811365806 | 25.6 MB
This book explores the diverse types of Schrödinger equations that appear in nonlinear systems in general, with a specific focus on nonlinear transmission networks and Bose-Einstein Condensates. In the context of nonlinear transmission networks, it employs various methods to rigorously model the phenomena of modulated matter-wave propagation in the network, leading to nonlinear Schrödinger (NLS) equations. Modeling these phenomena is largely based on the reductive perturbation method, and the derived NLS equations are then used to methodically investigate the dynamics of matter-wave solitons in the network. In the context of Bose-Einstein condensates (BECs), the book analyzes the dynamical properties of NLS equations with the external potential of different types, which govern the dynamics of modulated matter-waves in BECs with either two-body interactions or both two- and three-body interatomic interactions. It also discusses the method of investigating both the well-posedness and the ill-posedness of the boundary problem for linear and nonlinear Schrödinger equations and presents new results. Using simple examples, it then illustrates the results on the boundary problems. For both nonlinear transmission networks and Bose-Einstein condensates, the results obtained are supplemented by numerical calculations and presented as figures.

Free Download Schrödinger’s Cat Smile (Algorithms for Construction of Reality in Physics) by Sergey P. Suprun, Anatoly P. Suprun, Victor F. Petrenko
English | October 7, 2022 | ISBN: 9815049674 | 216 pages | MOBI | 3.40 Mb
The book presents a multidisciplinary analysis of the context of quantum physics experiments and the function of the human mind that makes it possible to demonstrate that an object-based model of reality formed at the level of the unconscious is the basis of our worldview.