Quantum Mechanics In Matrix Form

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Quantum Mechanics In Matrix Form

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Author : Günter Ludyk
language : en
Publisher: Springer
Release Date : 2017-10-25

Quantum Mechanics In Matrix Form written by Günter Ludyk and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-25 with Science categories.

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 Mechanics In Simple Matrix Form

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Author : Thomas F. Jordan
language : en
Publisher: Courier Corporation
Release Date : 2012-05-23

Quantum Mechanics In Simple Matrix Form written by Thomas F. Jordan and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-23 with Science categories.

With this text, basic quantum mechanics becomes accessible to undergraduates with no background in mathematics beyond algebra. Includes more than 100 problems and 38 figures. 1986 edition.

The Historical Development Of Quantum Theory

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Author : Jagdish Mehra
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-12-28

The Historical Development Of Quantum Theory written by Jagdish Mehra and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-12-28 with Science categories.

Quantum Theory, together with the principles of special and general relativity, constitute a scientific revolution that has profoundly influenced the way in which we think about the universe and the fundamental forces that govern it. The Historical Development of Quantum Theory is a definitive historical study of that scientific work and the human struggles that accompanied it from the beginning. Drawing upon such materials as the resources of the Archives for the History of Quantum Physics, the Niels Bohr Archives, and the archives and scientific correspondence of the principal quantum physicists, as well as Jagdish Mehra's personal discussions over many years with most of the architects of quantum theory, the authors have written a rigorous scientific history of quantum theory in a deeply human context. This multivolume work presents a rich account of an intellectual triumph: a unique analysis of the creative scientific process. The Historical Development of Quantum Theory is science, history, and biography, all wrapped in the story of a great human enterprise. Its lessons will be an aid to those working in the sciences and humanities alike.

The Matrix Perturbation Method In Quantum Mechanics

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Author : Francisco Soto-Eguibar
language : en
Publisher: Springer Nature
Release Date : 2024-02-20

The Matrix Perturbation Method In Quantum Mechanics written by Francisco Soto-Eguibar and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-02-20 with Science categories.

This book provides an alternative approach to time-independent perturbation theory in non-relativistic quantum mechanics. It allows easy application to any initial condition because it is based on an approximation to the evolution operator and may also be used on unitary evolution operators for the unperturbed Hamiltonian in the case where the eigenvalues cannot be found. This flexibility sets it apart from conventional perturbation theory. The matrix perturbation method also gives new theoretical insights; for example, it provides corrections to the energy and wave function in one operation. Another notable highlight is the facility to readily derive a general expression for the normalization constant at m-th order, a significant difference between the approach within and those already in the literature. Another unique aspect of the matrix perturbation method is that it can be extended directly to the Lindblad master equation. The first and second-order corrections are obtained for this equation and the method is generalized for higher orders. An alternative form of the Dyson series, in matrix form instead of integral form, is also obtained. Throughout the book, several benchmark examples and practical applications underscore the potential, accuracy and good performance of this novel approach. Moreover, the method's applicability extends to some specific time-dependent Hamiltonians. This book represents a valuable addition to the literature on perturbation theory in quantum mechanics and is accessible to students and researchers alike.

Special Matrices Of Mathematical Physics

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Author : Ruben Aldrovandi
language : en
Publisher: World Scientific
Release Date : 2001

Special Matrices Of Mathematical Physics written by Ruben Aldrovandi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.

Ch. 1. Some fundamental notions. 1.1. Definitions. 1.2. Components of a matrix. 1.3. Matrix functions. 1.4. Normal matrices -- ch. 2. Evolving systems -- ch. 3. Markov chains. 3.1. Non-negative matrices. 3.2. General properties -- ch. 4. Glass transition -- ch. 5. The Kerner model. 5.1. A simple example: Se-As glass -- ch. 6. Formal developments. 6.1. Spectral aspects. 6.2. Reducibility and regularity. 6.3. Projectors and asymptotics. 6.4. Continuum time -- ch. 7. Equilibrium, dissipation and ergodicity. 7.1. Recurrence, transience and periodicity. 7.2. Detailed balancing and reversibility. 7.3. Ergodicity -- ch. 8. Prelude -- ch. 9. Definition and main properties. 9.1. Bases. 9.2. Double Fourier transform. 9.3. Random walks -- ch. 10. Discrete quantum mechanics. 10.1. Introduction. 10.2. Weyl-Heisenberg groups. 10.3. Weyl-Wigner transformations. 10.4. Braiding and quantum groups -- ch. 11. Quantum symplectic structure. 11.1. Matrix differential geometry. 11.2. The symplectic form. 11.3. The quantum fabric -- ch. 12. An organizing tool -- ch. 13. Bell polynomials. 13.1. Definition and elementary properties. 13.2. The matrix representation. 13.3. The Lagrange inversion formula. 13.4. Developments -- ch. 14. Determinants and traces. 14.1. Introduction. 14.2. Symmetric functions. 14.3. Polynomials. 14.4. Characteristic polynomials. 14.5. Lie algebras invariants -- ch. 15. Projectors and iterates. 15.1. Projectors, revisited. 15.2. Continuous iterates -- ch. 16. Gases: real and ideal. 16.1. Microcanonical ensemble. 16.2. The canonical ensemble. 16.3. The grand canonical ensemble. 16.4. Braid statistics. 16.5. Condensation theories. 16.6. The Fredholm formalism.

A Modern Approach To Quantum Mechanics

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Author : John S. Townsend
language : en
Publisher: University Science Books
Release Date : 2000

A Modern Approach To Quantum Mechanics written by John S. Townsend and has been published by University Science Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Quantum theory categories.

Inspired by Richard Feynman and J.J. Sakurai, A Modern Approach to Quantum Mechanics allows lecturers to expose their undergraduates to Feynman's approach to quantum mechanics while simultaneously giving them a textbook that is well-ordered, logical and pedagogically sound. This book covers all the topics that are typically presented in a standard upper-level course in quantum mechanics, but its teaching approach is new. Rather than organizing his book according to the historical development of the field and jumping into a mathematical discussion of wave mechanics, Townsend begins his book with the quantum mechanics of spin. Thus, the first five chapters of the book succeed in laying out the fundamentals of quantum mechanics with little or no wave mechanics, so the physics is not obscured by mathematics. Starting with spin systems it gives students straightfoward examples of the structure of quantum mechanics. When wave mechanics is introduced later, students should perceive it correctly as only one aspect of quantum mechanics and not the core of the subject.

The Formulation Of Matrix Mechanics And Its Modifications 1925 1926

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Author : Jagdish Mehra
language : en
Publisher: Springer
Release Date : 1982-11-15

The Formulation Of Matrix Mechanics And Its Modifications 1925 1926 written by Jagdish Mehra and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982-11-15 with Science categories.

Quantum Theory, together with the principles of special and general relativity, constitute a scientific revolution that has profoundly influenced the way in which we think about the universe and the fundamental forces that govern it. The Historical Development of Quantum Theory is a definitive historical study of that scientific work and the human struggles that accompanied it from the beginning. Drawing upon such materials as the resources of the Archives for the History of Quantum Physics, the Niels Bohr Archives, and the archives and scientific correspondence of the principal quantum physicists, as well as Jagdish Mehra's personal discussions over many years with most of the architects of quantum theory, the authors have written a rigorous scientific history of quantum theory in a deeply human context. This multivolume work presents a rich account of an intellectual triumph: a unique analysis of the creative scientific process. The Historical Development of Quantum Theory is science, history, and biography, all wrapped in the story of a great human enterprise. Its lessons will be an aid to those working in the sciences and humanities alike.

Density Matrix Theories In Quantum Physics

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Author : Boris V. Bondarev
language : en
Publisher: Bentham Science Publishers
Release Date : 2020-11-03

Density Matrix Theories In Quantum Physics written by Boris V. Bondarev and has been published by Bentham Science Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-03 with Science categories.

In Density Matrix Theories in Quantum Physics, the author explores new possibilities for the main quantities in quantum physics – the statistical operator and the density matrix. The starting point in this exploration is the Lindblad equation for the statistical operator, where the main element of influence on a system by its environment is the dissipative operator. Bondarev has developed the theory of the harmonic oscillator, in which he finds the density matrix and proves the Heisenberg relation. Bondarev has written the dissipative diffusion and attenuation operators and proven the equivalence of the Wigner and Fokker–Planck equations using them. He further develops theories of the light-emitting diode and ball lightning. Bondarev also derives equations for the density matrix of a single particle and a system of identical particles. These equations have a remarkable property: when the density matrix has a diagonal shape they turn into a quantum kinetic equation for probability. Additional chapters in the book present new theories of experimentally discovered phenomena, such as the step kinetics of bimolecular reactions in solids, superconductivity, superfluidity, the energy spectrum of an arbitrary atom, lasers, spasers, and graphene. Density Matrix Theories in Quantum Physics is an informative reference for theoretical physicists interested in new theories on the subject of complex physical phenomena, quantum theory and density matrices.

Quantum Mechanics

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Author : Edward G Steward
language : en
Publisher: World Scientific Publishing Company
Release Date : 2011-10-18

Quantum Mechanics written by Edward G Steward and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-18 with Science categories.

This book provides the reader with an explanation of the origin and establishment of quantum mechanics together with a descriptive survey of developments up to the present day. The mathematics is presented in a digestible form yet following the original approach. This second edition presents two new chapters to supplement and extend the first edition material. “Interpretations of Quantum Mechanics” surveys a wide range of current topics, including the multiverse, 't Hooft's ideas for a deterministic local field theory, a summary of the de Broglie-Bohm pilot-wave theory and Anthony Valentini's development of it, and speculative concluding comments on the way ahead. “A Reflective Interlude” looks in more detail than hitherto at the origin and early years of wave-particle duality, with emphasis on trying to discover, as far as possible, what was the physical reality implied by de Broglie's work as it progressed. Appendices include useful reminder notes on associated background topics, with a new appendix “Planck Units”. With references to the original works, to reviews and useful bibliographies, the reader is uniquely well-equipped to delve further into the subject. In addition to its importance for those studying physics, this book is also intended for those studying the history of science. Contents: Setting the SceneLight: The 'Aether' and the Special Theory of RelativityThermal Radiation and Planck's 'Energy Elements'Einstein and the QuantumThe Quantum in the Atom: Optical SpectraEinstein's Transition Probabilities: Bohr's Theory and Planck's LawWave MechanicsMatrix MechanicsComplementarity, the Uncertainty Principle, and the Copenhagen InterpretationIndeterminacy and Entanglement (Sara M McMurry)A Reflective InterludeInterpretations of Quantum Mechanics (Sara M McMurry) Readership: Physicists, theoretical physicists, science historians and physical chemists.

Linear Operators For Quantum Mechanics

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Author : Thomas F. Jordan
language : en
Publisher: Courier Corporation
Release Date : 2012-09-20

Linear Operators For Quantum Mechanics written by Thomas F. Jordan and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-20 with Science categories.

Suitable for advanced undergraduates and graduate students, this compact treatment examines linear space, functionals, and operators; diagonalizing operators; operator algebras; and equations of motion. 1969 edition.