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Tutorial of quantum mechanics. By an experienced tutor ‒ for students of mathematics and physics. (Tutorium Quantenmechanik. Von einem erfahrenen Tutor ‒ für Physik- und Mathematikstudenten.) (German)
Heidelberg: Springer Spektrum (ISBN 978-3-642-37791-4/pbk; 978-3-642-37792-1/ebook). xi, 368~p. (2013).
The title “Tutorium Quantenmechanik” reflects very precisely the style and the content of the book written by Jan-Markus Schwindt. It is a publication of a great methodological work made by an experienced tutor. This book is a mixture of a textbook, a manual, a book of problems and a popular science bestseller. The book is addressed to students studying quantum mechanics, i.e. following the corresponding lecture course or reading a textbook of the classical style. The aim of Jan-Markus Schwindt is, in one hand, to make a standard material vivid, clear and interesting, on the other hand, to expand horizons going beyond the standard topics and outlining connections between different subjects. Opening this book (probably after a boring, too formal and abstract lecture) a reader gets into a classroom, where in a confidential and comfortable atmosphere he/she communicates with a friendly, open for any questions, well-educated person with a big sense of humor and! a passion for science. The book is easy and pleasant to read. It could be very helpful during the studies, in preparations to exams and even much after, e.g., for tutors themselves. The author in all details handles basic notions and concepts of quantum mechanics. Discussing each particular topic, he starts first with definitions and properties of related mathematical objects, then gives physical interpretations and analyzes the consequences. In the process he illustrates everything on the simplest problems and gives easy tasks to solve, questions for self-checking and remarks for advanced students. Sometimes such remarks lead even to small auxiliary Sections called “Streber-Ecke”. The book is enriched with solutions to all problems and funny pictures reflecting the “status quo” (see, e.g., the frontpage). It is worth to mention however, that this book is not a substitution of a standard textbook (or a standard lecture course). The author didn’t intend to expose all the material uniformly. So, some topics are just outlined or mentioned. And a style of a friendly conversation between a student and a tutor doesn’t suppose precise and concise formulations. This leads sometimes to inaccuracies (e.g., defining an eigenvector, the author didn’t mention that it must be nonzero) or even to mistakes (e.g., the author states on the page 94 that each $L^2$-function vanishes at infinity), but such events occur quite rare, fortunately. The book contains three parts. The first part is an introduction and a discussion of basic notions and concepts first in finite-dimensional, then in infinite-dimensional setting. The author also very honestly and a bit ironically presents his point of view concerning different interpretations of quantum mechanics. Part 2 is devoted to a scalar particle in an external potential. The author discusses in all details one-, two- and three-dimensional cases for different types of the potential and also the scattering theory. Part 3 contains more advanced topics: mathematical background for dealing with spin, a particle in a magnetic field, perturbation theory, many-particle systems. The author presents also such objects as path integrals and discusses relativistic setting of quantum mechanics.
Reviewer: Yana Kinderknecht (Völklingen)
Classification: M55
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