In this post, we will see the LaTeX version of the book Basic Concepts of Quantum Mechanics by Lev Tarasov. We had earlier seen a scanned version of the book.
About the book
This book gives a detailed and systematic exposition of the fundamentals of non-relativistic quantum mechanics for those who are not acquainted with the subject. The character of the physics of microparticles and the problems of the physics of microphenomena (interference of amplitudes, the principle of superposition, the specific nature of measuring processes, causality in quantum mechanics) are considered on the basis of concepts about probability amplitudes. Besides, the quantum-mechanical systems – microparticles – with two basic states are analyzed in detail. The apparatus of quantum mechanics is considered as a synthesis of concepts about physics and the theory of linear operators. A number of specially worked out problems and examples have been included in order to demonstrate the working of the apparatus.
This book is meant for use by students of engineering and teachers-training institutes. It may also be used by engineers of different profiles.
The book was translated from Russian by Ram Wadhwa and was originally published in 1980.
It took some time to complete this project (~4 years, on and off working on it), but I feel it was worth it. I have used the tufte-book class for the typesetting. The fonts used are Linux Libertine for serif and sans from the same family Linux Biolinum, the typewriter font is from Computer Modern family. The results are very satisfying and aesthetically pleasing. They are close to the original formatting in many ways, though not the same. I have tried my best to avoid any typos, though there might be still some remaining. If you find any typos or mistakes please do leave a comment. There is still a lot of scope fine tuning the document, adjusting spaces, placements etc., covers being made natively with TikZ , but that can wait for another release. Next in Tarasov’s books we will see The World is Built on Probability in the electronic format.
You can get the new copy of the book here .
You can get the LaTeX source files at: https://gitlab.com/mirtitles/tarasov-qm
Original scanned copy here.
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Some more snapshots from the new typesetting
Table of contents
Subject index (this took too long to make that I had anticipated)
Placing figures in the margins makes it easier.
Interludes have the take home points, and also present us with different worldviews while leading the discussions to next sections.
Prelude: Can the System of Classical Physics Concepts Be Considered Logically Perfect? 15
1 Physics of the Microparticles 21
1 Certain Characteristics and Properties of Microparticles 23
2 Two Fundamental Ideas of Quantum Mechanics 29
3 Uncertainty Relations 38
4 Some Results Ensuing from the Uncertainty Relations 45
5 Impossibility of Classical Representation of a Microparticle 51
6 Rejection of Ideas of Classical Physics 56
Interlude: Is a “Physically Intuitive” Model of a Microparticle Possible? 63
2 Physical Foundations of Quantum Mechanics 67
7 Some Basic Experiments 69
8 Amplitudes of Transition Probabilities (Formulation of Basic Principles) 78
9 Amplitudes of Transition Probabilities (Demonstration of Basic Principles) 83
10 Superposition of States 95
11 Measurement in Quantum Mechanics 104
Interlude: Are These the Same Waves?, Or, Again on Waves in Quantum Mechanics 112
12 Causality in Quantum Mechanics 115
13 Microparticles with Two Basic States 120
14 The Electron in a Magnetic Field 129
15 The Wave Function 135
16 Quantum Mechanics as a Qualitative Leap in Man’s Knowledge of the Laws of Nature 139
A Brief Interlude 147
Interlude: Do Quantum-Mechanical Concepts Contradict Our Common Sense? 153
3 Linear Operators in Quantum Mechanics 159
17 A Brief Look at the Theory of Linear Operators 162
18 From Hamiltonian Matrix to Energy Operator 170
19 Linear Operators in Quantum Mechanics 176
20 The Quantum-Mechanical Apparatus in Coordinate Representation 182
21 Applications of the Schrödinger Equation 192
22 The Hamiltonian in Some Specific Problems 204
23 Transition to the Momentum Representation 210
24 An Electron in a Periodic Field 215
25 The Probability of Quantum Transitions 222
26 Ways of Describing Evolution of Microsystems with Time 227
A Brief Historical Survey 233
A Eigenvalues and Eigenfunctions of a Hermitian Operator 244
B Transition from Quantum Mechanics to Classical Mechanics 245
C Commutation Relations 246
D Commutation of Operators 𝑀ˆ 2, 𝑀ˆ𝑖 248
E Some Special Functions 249
F Linear Harmonic Oscillator 252
Subject Index 255