A Mathematical Companion to Quantum MechanicsA Mathematical Companion to Quantum Mechanics



This original 2019 work, based on the author's many years of teaching at Harvard University, examines mathematical methods of value and importance to advanced undergraduates and graduate students studying quantum mechanics.

Author: Shlomo Sternberg

Publisher: Courier Dover Publications

ISBN: 9780486826899

Category:

Page: 336

View: 271

This original 2019 work, based on the author's many years of teaching at Harvard University, examines mathematical methods of value and importance to advanced undergraduates and graduate students studying quantum mechanics. Its intended audience is students of mathematics at the senor university level and beginning graduate students in mathematics and physics. Early chapters address such topics as the Fourier transform, the spectral theorem for bounded self-joint operators, and unbounded operators and semigroups. Subsequent topics include a discussion of Weyl's theorem on the essential spectrum and some of its applications, the Rayleigh-Ritz method, one-dimensional quantum mechanics, Ruelle's theorem, scattering theory, Huygens' principle, and many other subjects.

A Mathematical Companion to Quantum MechanicsA Mathematical Companion to Quantum Mechanics



Bibliographical Note A Mathematical Companion to Quantum Mechanics is a new work, first published by Dover Publications, Inc., in 2019. Library of Congress Cataloging-in-Publication Data Names: Sternberg, Shlomo, author.

Author: Shlomo Sternberg

Publisher: Courier Dover Publications

ISBN: 9780486839820

Category:

Page: 336

View: 954

This original 2019 work, based on the author's many years of teaching at Harvard University, examines mathematical methods of value and importance to advanced undergraduates and graduate students studying quantum mechanics. Its intended audience is students of mathematics at the senor university level and beginning graduate students in mathematics and physics. Early chapters address such topics as the Fourier transform, the spectral theorem for bounded self-joint operators, and unbounded operators and semigroups. Subsequent topics include a discussion of Weyl's theorem on the essential spectrum and some of its applications, the Rayleigh-Ritz method, one-dimensional quantum mechanics, Ruelle's theorem, scattering theory, Huygens' principle, and many other subjects.

The Mathematics CompanionThe Mathematics Companion



Mathematical Methods for Physicists and Engineers, 2nd Edition Anthony C. Fischer-Cripps. 3.5 Quantum Mechanics Summary Schrödinger equation ħ2 224 ay + V ( x , t ) ¥ = ih 2m Ox ? at Y ( x , t ) = v ( x ) ølt ) n2 a2y + Vy = Ey 2m ...

Author: Anthony C. Fischer-Cripps

Publisher: CRC Press

ISBN: 9781466515888

Category:

Page: 302

View: 717

Everything You Need to Know about Mathematics for Science and EngineeringUpdated and expanded with new topics, The Mathematics Companion: Mathematical Methods for Physicists and Engineers, 2nd Edition presents the essential core of mathematical principles needed by scientists and engineers. Starting from the basic concepts of trigonometry, the book

The Mathematics CompanionThe Mathematics Companion



Mathematical Methods for Physicists and Engineers Anthony Craig Fischer-Cripps. 2.8.2 Quantum mechanics + V 2 p Complex functions arise frequently in quantum mechanics . The total energy of a system is the sum of the potential and ...

Author: Anthony Craig Fischer-Cripps

Publisher: CRC Press

ISBN: 1420050761

Category:

Page: 210

View: 557

Following the style of The Physics Companion and The Electronics Companion, this book is a revision aid and study guide for undergraduate students in physics and engineering. It consists of a series of one-page-per-topic descriptions of the key concepts covered in a typical first-year "mathematics for physics" course. The emphasis is placed on relating the mathematical principles being introduced to real-life physical problems. In common with the other companions, there is strong use of figures throughout to help in understanding of the concepts under consideration. The book will be an essential reference and revision guide, particularly for those students who do not have a strong background in mathematics when beginning their degree.

A Mathematical Journey to Quantum MechanicsA Mathematical Journey to Quantum Mechanics



It is the companion book of "A Mathematical Journey to Relativity", by the same Authors, published by Springer in 2020. This book provides an itinerary to quantum mechanics taking into account the basic mathematics to formulate it.

Author: Salvatore Capozziello

Publisher: Springer

ISBN: 3030860973

Category:

Page: 289

View: 558

This book provides an itinerary to quantum mechanics taking into account the basic mathematics to formulate it. Specifically, it features the main experiments and postulates of quantum mechanics pointing out their mathematical prominent aspects showing how physical concepts and mathematical tools are deeply intertwined. The material covers topics such as analytic mechanics in Newtonian, Lagrangian, and Hamiltonian formulations, theory of light as formulated in special relativity, and then why quantum mechanics is necessary to explain experiments like the double-split, atomic spectra, and photoelectric effect. The Schrödinger equation and its solutions are developed in detail. It is pointed out that, starting from the concept of the harmonic oscillator, it is possible to develop advanced quantum mechanics. Furthermore, the mathematics behind the Heisenberg uncertainty principle is constructed towards advanced quantum mechanical principles. Relativistic quantum mechanics is finally considered.The book is devoted to undergraduate students from University courses of Physics, Mathematics, Chemistry, and Engineering. It consists of 50 self-contained lectures, and any statement and theorem are demonstrated in detail. It is the companion book of "A Mathematical Journey to Relativity", by the same Authors, published by Springer in 2020.

Exercises in Quantum MechanicsExercises in Quantum Mechanics



The present revised edition is more attractive in layout than its predecessor, and most, if not all of the errors in the original edition (many of which were kindly pointed out by reviewers, colleagues, and students) have now been corrected ...

Author: H.A. Mavromatis

Publisher: Springer Science & Business Media

ISBN: 079231557X

Category:

Page: 333

View: 133

This monograph is written within the framework of the quantum mechanical paradigm. It is modest in scope in that it is restricted to some observations and solved illustrative problems not readily available in any of the many standard (and several excellent) texts or books with solved problems that have been written on this subject. Additionally a few more or less standard problems are included for continuity and purposes of comparison. The hope is that the points made and problems solved will give the student some additional insights and a better grasp of this fascinating but mathematically somewhat involved branch of physics. The hundred and fourteen problems discussed have intentionally been chosen to involve a minimum of technical complexity while still illustrating the consequences of the quantum-mechanical formalism. Concerning notation, useful expressions are displayed in rectangular boxes while calculational details which one may wish to skip are included in square brackets. Beirut HARRY A. MAVROMATIS June, 1985 IX Preface to Second Edition More than five years have passed since I prepared the first edition of this mono graph. The present revised edition is more attractive in layout than its predecessor, and most, if not all of the errors in the original edition (many of which were kindly pointed out by reviewers, colleagues, and students) have now been corrected. Additionally the material in the original fourteen chapters has been extended with significant additions to Chapters 8, 13, and 14.

The Materials Physics Companion 2nd EditionThe Materials Physics Companion 2nd Edition



This edition illustrates how electrical and magnetic properties of matter arise from the basic principles of quantum mechanics in a way that is accessible to science and engineering students.

Author: Anthony C. Fischer-Cripps

Publisher: CRC Press

ISBN: 9781466517820

Category:

Page: 238

View: 311

Understand the Physics of the Solid State Updated and expanded with new topics, The Materials Physics Companion, 2nd Edition puts the physics of the solid state within the reach of students by offering an easy-to-navigate pathway from basic knowledge through to advanced concepts. This edition illustrates how electrical and magnetic properties of matter arise from the basic principles of quantum mechanics in a way that is accessible to science and engineering students. A Convenient, Student-Friendly Format Rich with Diagrams and Clear Explanations The book uses the unique signature style of the author’s other companion books, providing detailed graphics, simple and clear explanations of difficult concepts, and annotated mathematical treatments. It covers quantum mechanics, x-ray analysis, solid-state physics, the mechanical and thermal properties of solids, the electrical and magnetic properties of solids, and superconductivity, assuming no prior knowledge of these advanced areas. Suitable for undergraduate students in science and engineering, the book is also a handy refresher for professional scientists and educators. Be sure to check out the author’s other companion books: The Mathematics Companion: Mathematical Methods for Physicists and Engineers, 2nd Edition The Physics Companion, 2nd Edition The Electronics Companion: Devices and Circuits for Physicists and Engineers, 2nd Edition The Chemistry Companion

A Mathematical Journey to Quantum MechanicsA Mathematical Journey to Quantum Mechanics



After, we develop other lectures to move toward the axiomatic formalism of Quantum Mechanics. ... The philosophy we followed in writing this book is the same as that used for the companion book A Mathematical Journey to Relativity [1] ...

Author: Salvatore Capozziello

Publisher: Springer Nature

ISBN: 9783030860981

Category:

Page:

View: 597

Technology and MathematicsTechnology and Mathematics



Constructive mathematics and quantum mechanics: Unbounded operators and the spectral theorem. Journal of Philosophical Logic, ... In N. J. Higham (Ed.), The Princeton companion to applied mathematics. Princeton: Princeton University ...

Author: Sven Ove Hansson

Publisher: Springer

ISBN: 9783319937793

Category:

Page: 373

View: 388

This volume is the first extensive study of the historical and philosophical connections between technology and mathematics. Coverage includes the use of mathematics in ancient as well as modern technology, devices and machines for computation, cryptology, mathematics in technological education, the epistemology of computer-mediated proofs, and the relationship between technological and mathematical computability. The book also examines the work of such historical figures as Gottfried Wilhelm Leibniz, Charles Babbage, Ada Lovelace, and Alan Turing.