A Mathematical Journey to Quantum Mechanics

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Beschreibung

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.

Über den Autor

Wladimir-Georges Boskoff graduated at Faculty of Mathematics of the University of Bucharest in 1982 - PhD in 1994. Since 1990, he became Member of the Department of Mathematics and Informatics of Ovidius University of Constanta providing courses in Euclidean Geometry, Differential Geometry, Calculus on Manifolds, Mechanics and Relativity, Astronomy, History of Mathematics, Basic Quantum Mechanics, etc. Among his previous books, "A Mathematical Journey to Relativity" with Salvatore Capozziello, Springer, 2020, and "Discovering Geometry: An Axiomatic Approach" with Adrian Vijiac, Matrixrom, 2011/2014.

Salvatore Capozziello is Full Professor in Astronomy and Astrophysics at the Department of Physics of University of Naples "Federico II" and Former President of the Italian Society for General Relativity and Gravitation (SIGRAV). Since 2013, he is Professor Honoris Causa at the Tomsk State Pedagogical University (TSPU), Russian Federation. His scientific activity is devoted to research topics in general relativity, cosmology, relativistic astrophysics, and physics of gravitation in their theoretical and phenomenological aspects. His research interests are extended theories of gravity and their cosmological and astrophysical applications; large-scale structure of the universe; gravitational lensing; gravitational waves; galactic dynamics; quantum phenomena in a gravitational field; quantum cosmology. He published almost 600 scientific papers and 5 books.

Zusammenfassung

Facilitates learning presenting each topic from elementary-intermediate level to advanced

Shows that parallelism is continuously made between classical mechanics and quantum mechanics formalism

Gives proofs of theorems with all details necessary to understand

Inhaltsverzeichnis

Introduction: How to read this book.- Newtonian, Lagrangian and Hamiltonian Mechanics.- Can Light be described by Classical Mechanics?.- Why Quantum Mechanics?.- The Schrödinger Equations and Their Consequences.- The Mathematics behind the Harmonic Oscillator.- From Monochromatic Plane Waves to Wave Packets.- The Heisenberg Uncertainty Principle and the Mathematics behind.- The Principles of Quantum Mechanics.- Consequences of Quantum Mechanics Principles.- Quantum Mechanics at the Next Level.- Conclusions.

Details

Erscheinungsjahr:	2022
Fachbereich:	Theoretische Physik
Genre:	Mathematik , Medizin , Naturwissenschaften , Physik , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	xv 289 S. 10 farbige Illustr. 289 p. 10 illus. in color.
ISBN-13:	9783030861001
ISBN-10:	3030861007
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Boskoff, Wladimir-Georges Capozziello, Salvatore
Auflage:	1st edition 2021
Hersteller:	Springer International Publishing
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 17 mm
Von/Mit:	Wladimir-Georges Boskoff (u. a.)
Erscheinungsdatum:	29.09.2022
Gewicht:	0,47 kg

Artikel-ID: 124141583