Quantum Mechanics Upon Theorems

Author : Fu-sui Liu
Publisher : Unknown
Page : 0 pages
File Size : 50,8 Mb
Release : 2014
Category : Quantum theory
ISBN : 1629485861

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Advanced Quantum Mechanics Upon Theorems by Fu-sui Liu Pdf

Rather than the ordinary axiomatic approach to establish advanced quantum mechanics and badic quantum field theory upon postulates, in chapter 1 author introduces the 52 theorems, 16 corollaries, one criterion, and one law in "Quantum Mechanics upon Theorems", and prove two new theorems (Big theorem of energy and big theorem of wavepacket). In the other 9 chapters, this textbook proves 20 new theorems and 7 corollaries. For example, the commutation relations between field and field momentum are given by a theorem, and a convenient method to treat field quantisation of constrained system is given by a corollary.

Author : Fu-sui Liu
Publisher : Nova Science Publishers
Page : 0 pages
File Size : 52,5 Mb
Release : 2013
Category : Quantum theory
ISBN : 1628086858

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Quantum Mechanics Upon Theorems by Fu-sui Liu Pdf

This innovative new textbook contains forty-nine theorems, sixteen corollaries, one criterion, and one law, and thus for the first time, approaches quantum mechanics in a manner to be established on the basis of exact proofs instead of on postulates, principles, axioms, hypotheses, assumptions, and guesses, and in a manner to be free from paradoxes. In this textbook, most chapters start with a bit of history, because the historical experiences are worthy to note. All the difficult points, such as the wave-particle duality and uncertainty relations and operator representation of the observable are proved exactly by mathematics, and thus the concepts and pictures in quantum mechanics become easy to understand and imagine. If readers understand the preparations for analytical mechanics and mathematics in Chapter Two, then they can understand quantum mechanics without a lot of difficulties. This textbook makes quantum mechanics go from covered in a mysterious veil to the uncovered truth. The author would like to predict that there will be a day certainly that this textbook becomes a standard textbook of quantum mechanics in our world.

Author : Gianfausto Dell'Antonio
Publisher : Springer
Page : 459 pages
File Size : 41,9 Mb
Release : 2015-05-25
Category : Science
ISBN : 9789462391185

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Lectures on the Mathematics of Quantum Mechanics I by Gianfausto Dell'Antonio Pdf

The first volume (General Theory) differs from most textbooks as it emphasizes the mathematical structure and mathematical rigor, while being adapted to the teaching the first semester of an advanced course in Quantum Mechanics (the content of the book are the lectures of courses actually delivered.). It differs also from the very few texts in Quantum Mechanics that give emphasis to the mathematical aspects because this book, being written as Lecture Notes, has the structure of lectures delivered in a course, namely introduction of the problem, outline of the relevant points, mathematical tools needed, theorems, proofs. This makes this book particularly useful for self-study and for instructors in the preparation of a second course in Quantum Mechanics (after a first basic course). With some minor additions it can be used also as a basis of a first course in Quantum Mechanics for students in mathematics curricula. The second part (Selected Topics) are lecture notes of a more advanced course aimed at giving the basic notions necessary to do research in several areas of mathematical physics connected with quantum mechanics, from solid state to singular interactions, many body theory, semi-classical analysis, quantum statistical mechanics. The structure of this book is suitable for a second-semester course, in which the lectures are meant to provide, in addition to theorems and proofs, an overview of a more specific subject and hints to the direction of research. In this respect and for the width of subjects this second volume differs from other monographs on Quantum Mechanics. The second volume can be useful for students who want to have a basic preparation for doing research and for instructors who may want to use it as a basis for the presentation of selected topics.

Author : Brian C. Hall
Publisher : Springer Science & Business Media
Page : 554 pages
File Size : 49,5 Mb
Release : 2013-06-19
Category : Science
ISBN : 9781461471165

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Quantum Theory for Mathematicians by Brian C. Hall Pdf

Although ideas from quantum physics play an important role in many parts of modern mathematics, there are few books about quantum mechanics aimed at mathematicians. This book introduces the main ideas of quantum mechanics in language familiar to mathematicians. Readers with little prior exposure to physics will enjoy the book's conversational tone as they delve into such topics as the Hilbert space approach to quantum theory; the Schrödinger equation in one space dimension; the Spectral Theorem for bounded and unbounded self-adjoint operators; the Stone–von Neumann Theorem; the Wentzel–Kramers–Brillouin approximation; the role of Lie groups and Lie algebras in quantum mechanics; and the path-integral approach to quantum mechanics. The numerous exercises at the end of each chapter make the book suitable for both graduate courses and independent study. Most of the text is accessible to graduate students in mathematics who have had a first course in real analysis, covering the basics of L2 spaces and Hilbert spaces. The final chapters introduce readers who are familiar with the theory of manifolds to more advanced topics, including geometric quantization.

Author : Anatolij Dvurecenskij
Publisher : Springer Science & Business Media
Page : 338 pages
File Size : 43,9 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9789401582223

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Gleason's Theorem and Its Applications by Anatolij Dvurecenskij Pdf

For many years physics and mathematics have had a fruitful influence on one another. Classical mechanics and celestial mechanics have produced very deep problems whose solutions have enhanced mathematics. On the other hand, mathematics itself has found interesting theories which then (sometimes after many years) have been reflected in physics, confirming the thesis that nothing is more practical than a good theory. The same is true for the younger physical discipline -of quantum mechanics. In the 1930s two events, not at all random, became: The mathematical back grounds of both quantum mechanics and probability theory. In 1936, G. Birkhoff and J. von Neumann published their historical paper "The logic of quantum mechanics", in which a quantum logic was suggested. The mathematical foundations of quantum mechanics remains an outstanding problem of mathematics, physics, logic and philosophy even today. The theory of quantum logics is a major stream in this axiomatical knowledge river, where L(H), the system of all closed subspaces of a Hilbert space H, due to J. von Neumann, plays an important role. When A.M. Gleason published his solution to G. Mackey's problem showing that any state (= probability measure) corresponds to a density operator, he probably did not anticipate that his solution would become a cornerstone of ax iomati cal theory of quantum mechanics nor that it would provide many interesting applications to mathematics.

Author : K.R. Parthasarathy
Publisher : Springer
Page : 175 pages
File Size : 51,7 Mb
Release : 2005-10-15
Category : Mathematics
ISBN : 9789386279286

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Mathematical Foundation of Quantum Mechanics by K.R. Parthasarathy Pdf

This is a brief introduction to the mathematical foundations of quantum mechanics based on lectures given by the author to Ph.D.students at the Delhi Centre of the Indian Statistical Institute in order to initiate active research in the emerging field of quantum probability. The material in the first chapter is included in the author's book "An Introduction to Quantum Stochastic Calculus" published by Birkhauser Verlag in 1992 and the permission of the publishers to reprint it here is acknowledged. Apart from quantum probability, an understanding of the role of group representations in the development of quantum mechanics is always a fascinating theme for mathematicians. The first chapter deals with the definitions of states, observables and automorphisms of a quantum system through Gleason's theorem, Hahn-Hellinger theorem and Wigner's theorem. Mackey's imprimitivity theorem and the theorem of inducing representations of groups in stages are proved directly for projective unitary antiunitary representations in the second chapter. Based on a discussion of multipliers on locally compact groups in the third chapter all the well-known observables of classical quantum theory like linear momenta, orbital and spin angular momenta, kinetic and potential energies, gauge operators etc., are derived solely from Galilean covariance in the last chapter. A very short account of observables concerning a relativistic free particle is included. In conclusion, the spectral theory of Schrodinger operators of one and two electron atoms is discussed in some detail.

Author : Horst R. Beyer
Publisher : Springer Nature
Page : 222 pages
File Size : 54,7 Mb
Release : 2024-05-31
Category : Electronic
ISBN : 9783031490781

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Introduction to Quantum Mechanics by Horst R. Beyer Pdf

Author : Pankaj Sharan
Publisher : Springer Nature
Page : 115 pages
File Size : 47,9 Mb
Release : 2020-10-27
Category : Science
ISBN : 9783030604189

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Some Unusual Topics in Quantum Mechanics by Pankaj Sharan Pdf

In this book, the author addresses selected topics in quantum mechanics that are not usually covered in books, but which are very helpful in developing a student's interest in, and a deeper understanding of the subject. The topics include two different ways of looking at quantum mechanics; three clarifying topics that students often find confusing; one classic theorem never proved in the classroom; and a discussion on whether there can be a non-linear quantum mechanics. The book can be used as supporting material for graduate-level core courses on quantum mechanics.

Author : Menas Kafatos
Publisher : Springer Science & Business Media
Page : 314 pages
File Size : 43,7 Mb
Release : 2013-03-09
Category : Science
ISBN : 9789401708494

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Bell's Theorem, Quantum Theory and Conceptions of the Universe by Menas Kafatos Pdf

Bell's Theorem and its associated implications for the nature of the physical world remain topics of great interest. For this reason many meetings have been recently held on the interpretation of quantum theory and the implications of Bell's Theorem. Generally these meetings have been held primarily for quantum physicists and philosophers of science who have been or are actively working on the topic. Nevertheless, other philosophers of science, mathematicians, engineers as well as members of the general public have increasingly taken interest in Bell's Theorem and its implications. The Fall Workshop held at George Mason University on October 21 and 22, 1988 and titled "Bell's Theorem, Quantum Theory and Conceptions of the Universe" was of a more general scope. Not only it attracted experts in the field, it also covered other topics such as the implications of quantum non-locality for the nature of consciousness, cosmology, the anthropic principle, etc. topics usually not covered in previous meetings of this kind. The meeting was attended by more than one hundred ten specialists and other interested people from all over the world. The purpose of the meeting was not to provide a definitive answer to the general questions raised by Bell's Theorem. It is likely that the debate will go on for quite a long time. Rather, it was meant to contribute to the important dialogue between different disciplines.

Author : Mary Bell,Shan Gao
Publisher : Cambridge University Press
Page : 459 pages
File Size : 55,6 Mb
Release : 2016-09-19
Category : Science
ISBN : 9781107104341

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Quantum Nonlocality and Reality by Mary Bell,Shan Gao Pdf

A collaboration between distinguished physicists and philosophers of physics, this important anthology surveys the deep implications of Bell's nonlocality theorem.

Author : John D. McGervey
Publisher : Academic Press
Page : 408 pages
File Size : 50,7 Mb
Release : 2013-10-22
Category : Science
ISBN : 9781483288857

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Quantum Mechanics by John D. McGervey Pdf

This re-focused third edition of McGerveys Introduction to Modern Physics is one of the most comprehensive up-to-date textbooks and references sources on quantum mechanics available. This revision fills the gapbetween the mainly descriptive treatments of quantum mechanics, usually found in traditional modern physics texts, and the non-intuitive approaches that treat the subject as a series of mathematical theorems. McGervey achieves this goal with a thoughtfulanalysis of a number of experiments, supplementing these with fully worked examples, and by investigating paradoxes rather than relying on the analysis of a series of dry mathematical theorems. Software, provided with the text, is available for IBM-PC compatible computers with VGA graphics. The software is the basis for the homework problems, many of which have not been used in any form in other books at this level. The text is exceptionally current, a fact reflected in the significant amount of materialbased on articles published in recent years in The American Journal of Physics, The Physical Review, and Science. In all, McGervey provides a lively discussion that will motivate interest and understanding of the subject at the senior undergraduate level. * A re-focused third edition of McGervey's Introduction to Modern Physics * Analyzes a number of different experiments, supplementing these with numerical examples including fully worked problems * Includes software that is the basis for homework problems, many of which have not been seen in any other form in other books at this level * Investigates paradoxes rather than relying on the analysis of a series of dry mathematical theorems

Author : M. Ferrero,Alwyn van der Merwe
Publisher : Springer Science & Business Media
Page : 447 pages
File Size : 48,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789401158862

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New Developments on Fundamental Problems in Quantum Physics by M. Ferrero,Alwyn van der Merwe Pdf

Quantum theory is one of the most fascinating and successful constructs in the intellectual history of mankind. Nonetheless, the theory has very shaky philosophical foundations. This book contains thoughtful discussions by eminent researchers of a spate of experimental techniques newly developed to test some of the stranger predictions of quantum physics. The advances considered include recent experiments in quantum optics, electron and ion interferometry, photon down conversion in nonlinear crystals, single trapped ions interacting with laser beams, atom-field coupling in micromaser cavities, quantum computation, quantum cryptography, decoherence and macroscopic quantum effects, the quantum state diffusion model, quantum gravity, the quantum mechanics of cosmology and quantum non-locality along with the continuing debate surrounding the interpretation of quantum mechanics. Audience: The book is intended for physicists, philosophers of science, mathematicians, graduate students and those interested in the foundations of quantum theory.

Author : F Strocchi
Publisher : World Scientific Publishing Company
Page : 160 pages
File Size : 51,5 Mb
Release : 2005-11-17
Category : Science
ISBN : 9789813106598

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An Introduction to the Mathematical Structure of Quantum Mechanics by F Strocchi Pdf

This book arises out of the need for Quantum Mechanics (QM) to be part of the common education of mathematics students. Rather than starting from the Dirac–Von Neumann axioms, the book offers a short presentation of the mathematical structure of QM using the C–-algebraic structure of the observable based on the operational definition of measurements and the duality between states and observables. The description of states and observables as Hilbert space vectors and operators is then derived from the GNS and Gelfand-Naimark Theorems. For finite degrees of freedom, the Weyl algebra codifies the experimental limitations on the measurements of position and momentum (Heisenberg uncertainty relations) and Schroedinger QM follows from the von Neumann uniqueness theorem. The existence problem of the dynamics is related to the self-adjointness of the differential operator describing the Hamiltonian and solved by the Rellich–Kato theorems. Examples are discussed which include the explanation of the discreteness of the atomic spectra. Because of the increasing interest in the relation between QM and stochastic processes, a final chapter is devoted to the functional integral approach (Feynman–Kac formula), the formulation in terms of ground state correlations (Wightman functions) and their analytic continuation to imaginary time (Euclidean QM). The quantum particle on a circle as an example of the interplay between topology and functional integral is also discussed in detail.

Author : H-D Doebner,S T Ali,M Keyl,R F Werner
Publisher : World Scientific
Page : 300 pages
File Size : 40,7 Mb
Release : 2000-01-22
Category : Science
ISBN : 9789814543347

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Trends in Quantum Mechanics by H-D Doebner,S T Ali,M Keyl,R F Werner Pdf

Contents:Relationships Between q-Deformations, Typical Length Scales and Lower Measurability Bounds (E Papp)Description of Kerr States via Deformed Bosons (A I Solomon et al.)Quantum Mechanics on Phase Spaces ZN x ZN (J Tolar)Continuous Fuzzy Measurement of Energy: Realization and Application (J Audretsch)Decoherence and the Final Pointer Basis (M Castagnino & R Laura)On Hybrid Dynamics of the Copenhagen Dichotomic World (L Diósi)Storage and Read-Out of Quantum-State Information via Interference (M Freyberger et al.)Is There a Gravitational Collapse of the Wave-Packet? (H-J Schmidt)Operators and Maps Affiliated to EPR Channels (A Uhlmann)Reconstruction of Quantum States and Its Conceptual Implications (S Weigert)Geometric Formulation of Nonlinear Quantum Mechanics for Density Matrices (P Bóna)Fundamental Principles of Quantum Mechanics and Non(Linearity) (R Cirelli et al.)Nonlinear von Neumann-Type Equations (M Czachor et al.)Some Aspects of Nonlinearity and Gauge Transformation in Quantum Mechanics (G A Goldin)On a Theorem of Ashtekar and Lewandowski in the Mathematical Framework of Canonical Quantization in Quantum Gravity (H Baumgärtel)The Fuzzy (Super)Sphere and Field Theory (H Grosse & G Reiter)Quantum Fields Along Worldlines (M Keyl)Field Theory Revisited (C Piron)and other papers Readership: Mathematical physicists. Keywords:

Author : Partha Ghose
Publisher : Cambridge University Press
Page : 226 pages
File Size : 53,5 Mb
Release : 1999-04-29
Category : Science
ISBN : 9780521554633

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Testing Quantum Mechanics on New Ground by Partha Ghose Pdf

Simple accounts of experiments which test the counterintuitive and bizarre consequences of quantum theory.