A Mathematical Journey to Quantum Mechanics

Salvatore Capozziello, Wladimir-Georges Boskoff (Autoren)

Buch | Hardcover

XV, 289 Seiten

2021 | 1st ed. 2021
Springer International Publishing (Verlag)
978-3-030-86097-4 (ISBN)

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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.

Wladimir-Georges Boskoff is graduates Faculty of Mathematics of the University of Bucharest in 1982 - PhD in 1994. Since 1990, he became Member of the Department of Mathematics providing courses in Euclidean and Non-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 Universit di Napoli "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.

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.

Erscheinungsdatum	29.09.2021
Reihe/Serie	UNITEXT for Physics
Zusatzinfo	XV, 289 p. 10 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	619 g
Themenwelt	Naturwissenschaften ► Physik / Astronomie ► Atom- / Kern- / Molekularphysik
	Naturwissenschaften ► Physik / Astronomie ► Quantenphysik
	Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
Schlagworte	analytic mechanics • Elementary Particles, Quantum Field Theory • Functional Analysis • hamiltonian mechanics • Lagrangian mechanics • Operator algebra • Quantum Theory • Textbook in Quantum Mechanics • Theoretical Particle Physics
ISBN-10	3-030-86097-3 / 3030860973
ISBN-13	978-3-030-86097-4 / 9783030860974
Zustand	Neuware