# A Condensed Course of Quantum Mechanics

**subjects:**
science – physics, mathematics and statistics

e-book, 1. edition

**published:** june 2015

**ISBN:** 978-80-246-2349-8

**e-book formats** PDF

**recommended price:** 170 czk

### summary

This book represents a concise summary of non-relativistic quantum mechanics on the level suitable for university students of physics. It covers, perhaps even slightly exceeds, a one-year course of about 50 lectures, requiring basic knowledge of calculus, algebra, classical mechanics and a bit of motivation for the quantum adventure.

The exposition is succinct, with minimal narration, but with

a maximum of explicit and hierarchically structured mathematical derivations. The text covers all essential topics of university courses of quantum mechanics – from general mathematical formalism to specific applications. The formulation of quantum theory is accompanied by illustrations of the general concepts of elementary quantum systems. Some subtleties of mathematical foundations are overviewed, but the formalism is used in an accessible, intuitive way. Besides the traditional topics of non-relativistic quantum mechanics, such as single-particle dynamics, symmetries, semiclassical and perturbative approximations, density-matrix formalism, scattering theory, theory of angular momentum, description of

many-particle systems – the course also touches upon some modern issues, including quantum entanglement, decoherence, measurement, nonlocality, and quantum information. Historical context and chronology of basic achievements is outlined in brief remarks. The book is intended for beginners as a supplement to lectures, however, it may also be used by more advanced students as a compact and comprehensible overview of elementary quantum

theory.

### reviews

The text represents a remarkable attempt to provide comprehensive lecture notes in quantum 'mechanics (QM) that would avoid "too many words" and prefer instead mathematical language whenever possible. It covers (in fact slightly exceeds) a two-semester course designed for the 3rd year of the standard physics curriculum at the Faculty of Mathematics and Physics of the Charles University in Prague. The author taught such a course several times during recent years, so it is clear that the text already contains some feedback from the students and other interested people. As noted above, it is conceived as a rather technical guide through the lectures, with minimum of literary prose, so there is no "preparatory" historical chapter that would facilitate the mental passage of an uninitiated reader from the classical physics to the quantum world. This, of course, is by now the standard approach. Nevertheless, each chapter of the text is supplemented with a brief chronology of the essential achievements in the considered area; these historical remarks are really very helpful and instructive, since such an information is often quite difficult to find in common textbooks.

As to the contents, the material encompasses all traditional topics of the university QM courses (basics of the formalism of Hilbert spaces, representation of operators, quantum time evolution, systems of identical particles, symmetries, theory of angular momentum, basics of scattering theory, approximation methods, introduction to the Feynman path integral method). However, as an additional bonus, the author devotes a large space also to the discussion of the fundamental problems of the quantum measurement and related topics (EPR situation, hidden variables, Bell inequalities, quantum nonlocality). The concept of "entangled state" is discussed at some length and possible applications of quantum measurement are explained (quantum cryptography, teleportation and computation). The part of the text devoted to these themes contains more prose than the more traditional sections (where mathematical formulae constitute the prevailing language) and this is certainly beneficial for the potential reader interested primarily in modern problems of quantum information.

Overall, I find the present attempt at a "condensed QM course" to be quite successful. Although some parts are really rather terse, one may find excuse for it in the famous classic quotation that "the book of Nature is written in the language of mathematics". On the other hand, the text contains a lot of relevant material and its total amount certainly exceeds an average two-semester QM curriculum - this I can confirm with confidence based on my own experience with teaching QM in the past. Such an extension is in fact another profitable feature of this work, since it enables the lecturer to choose an appropriate mixture of relevant topics adjusted to the needs of the real audience.

I really recommend the text not only to physics students, but also to other lecturers, who may find here new impulses and motivation for updating and refreshing their courses.

Jiří Hořejší

I had pleasure reading this book. As advertised in the title, it is "condensed", and covers indeed a lot of material in only two hundred pages. Of course, it is meant to accompany an ordinary set of oral lectures, and /or may be read together with more detailed manuals, where complementary explanations can be found. But the "essence" is there. I found particularly interesting the style of the presentation, the original and excellent selection of topics, and the numerous brief historical remarks. The text is succinct but not superficial: when one goes deeper into the reading, one finds a lot of inspiring remarks. The reader is alerted to the subtleties of the mathematical formulation of quantum mechanics, without getting lost into unnecessary formalism. Modern issues concerning the interpretation, the issues of decoherence and quantum measurement are well presented. The book ends with an accessible presentation of some basics of many-body theory. All along our curiosity is alerted. It is a good book to have at hand to refresh one's memory about various aspects of elementary quantum mechanics, and for the student an excellent companion to undergo the r exploration of a fascinating subject, whose mysteries and beauty are excellently conveyed.

Jean-Paul Blaizot