Born-Jordan Quantization
Born-Jordan Quantization

Author: Maurice A. de Gosson

Publisher: Springer

Published: 2016-01-11

Total Pages: 226

ISBN-13: 3319279025

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This book presents a comprehensive mathematical study of the operators behind the Born–Jordan quantization scheme. The Schrödinger and Heisenberg pictures of quantum mechanics are equivalent only if the Born–Jordan scheme is used. Thus, Born–Jordan quantization provides the only physically consistent quantization scheme, as opposed to the Weyl quantization commonly used by physicists. In this book we develop Born–Jordan quantization from an operator-theoretical point of view, and analyze in depth the conceptual differences between the two schemes. We discuss various physically motivated approaches, in particular the Feynman-integral point of view. One important and intriguing feature of Born-Jordan quantization is that it is not one-to-one: there are infinitely many classical observables whose quantization is zero.

The Development of Elementary Quantum Theory
The Development of Elementary Quantum Theory

Author: Herbert Capellmann

Publisher: Springer

Published: 2017-09-12

Total Pages: 98

ISBN-13: 3319618849

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This book traces the evolution of the ideas that eventually resulted in the elementary quantum theory in 1925/26. Further, it discusses the essential differences between the fundamental equations of Quantum Theory derived by Born and Jordan, logically comprising Quantum Mechanics and Quantum Optics, and the traditional view of the development of Quantum Mechanics. Drawing on original publications and letters written by the main protagonists of that time, it shows that Einstein’s contributions from 1905 to 1924 laid the essential foundations for the development of Quantum Theory. Einstein introduced quantization of the radiation field; Born added quantized mechanical behavior. In addition, Born recognized that Quantum Mechanics necessarily required Quantum Optics; his radical concept of truly discontinuous and statistical quantum transitions (“quantum leaps”) was directly based on Einstein’s physical concepts.

The Strange World of Quantum Mechanics
The Strange World of Quantum Mechanics

Author: Daniel F. Styer

Publisher: Cambridge University Press

Published: 2000-02-24

Total Pages: 248

ISBN-13: 1316101878

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This is an exceptionally accessible, accurate, and non-technical introduction to quantum mechanics. After briefly summarizing the differences between classical and quantum behaviour, this engaging account considers the Stern-Gerlach experiment and its implications, treats the concepts of probability, and then discusses the Einstein-Podolsky-Rosen paradox and Bell's theorem. Quantal interference and the concept of amplitudes are introduced and the link revealed between probabilities and the interference of amplitudes. Quantal amplitude is employed to describe interference effects. Final chapters explore exciting new developments in quantum computation and cryptography, discover the unexpected behaviour of a quantal bouncing-ball, and tackle the challenge of describing a particle with no position. Thought-provoking problems and suggestions for further reading are included. Suitable for use as a course text, The Strange World of Quantum Mechanics enables students to develop a genuine understanding of the domain of the very small. It will also appeal to general readers seeking intellectual adventure.

Topics in Quantum Mechanics
Topics in Quantum Mechanics

Author: Floyd Williams

Publisher: Springer Science & Business Media

Published: 2003-01-23

Total Pages: 420

ISBN-13: 9780817643119

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This self-contained text presents quantum mechanics from the point of view of some computational examples with a mixture of mathematical clarity often not found in texts offering only a purely physical point of view. Emphasis is placed on the systematic application of the Nikiforov-- Uvarov theory of generalized hypergeometric differential equations to solve the Schr"dinger equation and to obtain the quantization of energies from a single unified point of view.

Quantum Mechanics in Matrix Form
Quantum Mechanics in Matrix Form

Author: Günter Ludyk

Publisher: Springer

Published: 2017-10-25

Total Pages: 217

ISBN-13: 3319263668

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This book gives an introduction to quantum mechanics with the matrix method. Heisenberg's matrix mechanics is described in detail. The fundamental equations are derived by algebraic methods using matrix calculus. Only a brief description of Schrödinger's wave mechanics is given (in most books exclusively treated), to show their equivalence to Heisenberg's matrix method. In the first part the historical development of Quantum theory by Planck, Bohr and Sommerfeld is sketched, followed by the ideas and methods of Heisenberg, Born and Jordan. Then Pauli's spin and exclusion principles are treated. Pauli's exclusion principle leads to the structure of atoms. Finally, Dirac ́s relativistic quantum mechanics is shortly presented. Matrices and matrix equations are today easy to handle when implementing numerical algorithms using standard software as MAPLE and Mathematica.

Quantum Harmonic Analysis
Quantum Harmonic Analysis

Author: Maurice A. de Gosson

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2021-07-05

Total Pages: 247

ISBN-13: 3110722909

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Quantum mechanics is arguably one of the most successful scientific theories ever and its applications to chemistry, optics, and information theory are innumerable. This book provides the reader with a rigorous treatment of the main mathematical tools from harmonic analysis which play an essential role in the modern formulation of quantum mechanics. This allows us at the same time to suggest some new ideas and methods, with a special focus on topics such as the Wigner phase space formalism and its applications to the theory of the density operator and its entanglement properties. This book can be used with profit by advanced undergraduate students in mathematics and physics, as well as by confirmed researchers.

Time-Frequency Analysis of Operators
Time-Frequency Analysis of Operators

Author: Elena Cordero

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2020-09-21

Total Pages: 458

ISBN-13: 311053245X

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This authoritative text studies pseudodifferential and Fourier integral operators in the framework of time-frequency analysis, providing an elementary approach, along with applications to almost diagonalization of such operators and to the sparsity of their Gabor representations. Moreover, Gabor frames and modulation spaces are employed to study dispersive equations such as the Schrödinger, wave, and heat equations and related Strichartz problems. The first part of the book is addressed to non-experts, presenting the basics of time-frequency analysis: short time Fourier transform, Wigner distribution and other representations, function spaces and frames theory, and it can be read independently as a short text-book on this topic from graduate and under-graduate students, or scholars in other disciplines.

The Formation and Logic of Quantum Mechanics
The Formation and Logic of Quantum Mechanics

Author: Mitsuo Taketani

Publisher: World Scientific

Published: 2001

Total Pages: 350

ISBN-13: 9789812810113

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This book analyzes the intricate logical process through which the quantum theory was developed, and shows that the quantum mechanics thus established is governed by stereo-structural logic . The method of analysis is based on Mituo Taketani''s three-stage theory of scientific cognition, which was presented and developed in close connection with Yukawa''s theory of the meson. According to the three-stage theory, scientific cognition proceeds through a series of coiling turns of the phenomenological, substantialistic and essentialistic stages. The old quantum mechanics is shown to be in a substantialistic stage, followed by the quantum mechanics in the corresponding essentialistic stage. Sample Chapter(s). Chapter 1.1: Themodynamical Investigation of Black Body Radiation (206 KB). Chapter 1.2: Atomistic Investigations of Black Body Radiation (257 KB). Chapter 1.3: Einstein''s Light Quantum (261 KB). Chapter 1.4: The Light Quantum and the Theory of Relativity (158 KB). Chapter 1.1: Diffculties seen from Statistical Heat Theory (281 KB). Chapter 1.2: Molecular Theoretical Significance of the Planck Theory (236 KB). Chapter 1.3: Conflict between the Wave and Particle Natures (235 KB). Chapter 1.1: Heisenbergs Quantum Condition (307 KB). Chapter 1.2: Born-Jordan''s Formulation with Matrices (361 KB). Chapter 1.3: Dirac''s Formulation by Quantum Algebra (299 KB). Chapter 1.4: Attempts at the Interpretation of Matrix Mechanics (272 KB). Contents: Volume I: Quantum of Radiation; The Formation of Atomic Models; Volume II: Difficulties in Radiation Theory; The Quantum of Action and Atomic Models; The Quantum Condition, Transition Probability and Correspondence Principle; Theory of Atomic Structure and Spin of Electron; The Interconnection of Wave- and Particle-Natures; Volume III: The Proposal and Formulation of Matrix Mechanics; From the Proposal of Wave Mechanics to Quantum Mechanics; The Establishment of Quantum Mechanics; The Logic of Quantum Mechanics. Readership: Undergraduates and researchers in quantum and theoretical physics.

Emergence Of The Quantum From The Classical: Mathematical Aspects Of Quantum Processes
Emergence Of The Quantum From The Classical: Mathematical Aspects Of Quantum Processes

Author: Maurice A De Gosson

Publisher: World Scientific

Published: 2017-11-10

Total Pages: 306

ISBN-13: 1786344165

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The emergence of quantum mechanics from classical world mechanics is now a well-established theme in mathematical physics. This book demonstrates that quantum mechanics can indeed be viewed as a refinement of Hamiltonian mechanics, and builds on the work of George Mackey in relation to their mathematical foundations. Additionally when looking at the differences with classical mechanics, quantum mechanics crucially depends on the value of Planck's constant h. Recent cosmological observations tend to indicate that not only the fine structure constant α but also h might have varied in both time and space since the Big Bang. We explore the mathematical and physical consequences of a variation of h; surprisingly we see that a decrease of h leads to transitions from the quantum to the classical.Emergence of the Quantum from the Classical provides help to undergraduate and graduate students of mathematics, physics and quantum theory looking to advance into research in the field.

Formation And Logic Of Quantum Mechanics, The (In 3 Vols)
Formation And Logic Of Quantum Mechanics, The (In 3 Vols)

Author: Masayuki Nagasaki

Publisher: World Scientific

Published: 2001-11-23

Total Pages: 915

ISBN-13: 9814491187

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This book analyzes the intricate logical process through which the quantum theory was developed, and shows that the quantum mechanics thus established is governed by stereo-structural logic. The method of analysis is based on Mituo Taketani's three-stage theory of scientific cognition, which was presented and developed in close connection with Yukawa's theory of the meson. According to the three-stage theory, scientific cognition proceeds through a series of coiling turns of the phenomenological, substantialistic and essentialistic stages. The old quantum mechanics is shown to be in a substantialistic stage, followed by the quantum mechanics in the corresponding essentialistic stage./a