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Quantum Mechanics for Pedestrians: Fundamentals 2014 ed., 1 [Minkštas viršelis]

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  • Formatas: Paperback / softback, 452 pages, aukštis x plotis: 235x155 mm, weight: 724 g, 23 black & white illustrations, 28 colour illustrations, 10 colour tables, biography
  • Serija: Undergraduate Lecture Notes in Physics
  • Išleidimo metai: 08-Nov-2013
  • Leidėjas: Springer International Publishing AG
  • ISBN-10: 3319007971
  • ISBN-13: 9783319007977
Kitos knygos pagal šią temą:
Quantum Mechanics for Pedestrians: Fundamentals 2014 ed., 1Didesnis paveikslėlis
  • Formatas: Paperback / softback, 452 pages, aukštis x plotis: 235x155 mm, weight: 724 g, 23 black & white illustrations, 28 colour illustrations, 10 colour tables, biography
  • Serija: Undergraduate Lecture Notes in Physics
  • Išleidimo metai: 08-Nov-2013
  • Leidėjas: Springer International Publishing AG
  • ISBN-10: 3319007971
  • ISBN-13: 9783319007977
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9783319007977.html
Raktažodžiai:
This book provides an introduction into the fundamentals of non-relativistic quantum mechanics. In Part 1, the essential principles are developed. Applications and extensions of the formalism can be found in Part 2. The book includes not only material that is presented in traditional textbooks on quantum mechanics, but also discusses in detail current issues such as interaction-free quantum measurements, neutrino oscillations, various topics in the field of quantum information as well as fundamental problems and epistemological questions, such as the measurement problem, entanglement, Bell's inequality, decoherence, and the realism debate. A chapter on current interpretations of quantum mechanics concludes the book. To develop quickly and clearly the main principles of quantum mechanics and its mathematical formulation, there is a systematic change between wave mechanics and algebraic representation in the first chapters. The required mathematical tools are introduced step by step. Moreover, the appendix collects compactly the most important mathematical tools that supplementary literature can be largely dispensed. In addition, the appendix contains advanced topics, such as Quantum- Zeno effect, time-delay experiments, Lenz vector and the Shor algorithm. About 250 exercises, most of them with solutions, help to deepen the understanding of the topics. Target groups of the book are student teachers and all students of physics, as minor or major, looking for a reasonably easy and modern introduction into quantum mechanics.

This book provides an introduction into the fundamentals of non-relativistic quantum mechanics. The first part of a two-volume reference, it develops essential principles and supports learning with exercises and problems with solutions.
Introduction xvii
Overview of Volume 1 xxiii
Part I Fundamentals
1 Towards the Schrodinger Equation
3(12)
1.1 How to Find a New Theory
3(2)
1.2 The Classical Wave Equation and the Schrodinger Equation
5(7)
1.2.1 From the Wave Equation to the Dispersion Relation
5(4)
1.2.2 From the Dispersion Relation to the Schrodinger Equation
9(3)
1.3 Exercises
12(3)
2 Polarization
15(14)
2.1 Light as Waves
16(7)
2.1.1 The Typical Shape of an Electromagnetic Wave
16(1)
2.1.2 Linear and Circular Polarization
17(2)
2.1.3 From Polarization to the Space of States
19(4)
2.2 Light as Photons
23(5)
2.2.1 Single Photons and Polarization
23(2)
2.2.2 Measuring the Polarization of Single Photons
25(3)
2.3 Exercises
28(1)
3 More on the Schrodinger Equation
29(12)
3.1 Properties of the Schrodinger Equation
29(2)
3.2 The Time-independent Schrodinger Equation
31(2)
3.3 Operators
33(6)
3.3.1 Classical Numbers and Quantum-Mechanical Operators
35(1)
3.3.2 Commutation of Operators; Commutators
36(3)
3.4 Exercises
39(2)
4 Complex Vector Spaces and Quantum Mechanics
41(14)
4.1 Norm, Bra-Ket Notation
42(2)
4.2 Orthogonality, Orthonormality
44(1)
4.3 Completeness
45(2)
4.4 Projection Operators, Measurement
47(6)
4.4.1 Projection Operators
47(4)
4.4.2 Measurement and Eigenvalues
51(1)
4.4.3 Summary
52(1)
4.5 Exercises
53(2)
5 Two Simple Solutions of the Schrodinger Equation
55(18)
5.1 The Infinite Potential Well
55(8)
5.1.1 Solution of the Schrodinger Equation, Energy Quantization
56(3)
5.1.2 Solution of the Time-Dependent Schrodinger Equation
59(1)
5.1.3 Properties of the Eigenfunctions and Their Consequences
60(2)
5.1.4 Determination of the Coefficients Cn
62(1)
5.2 Free Motion
63(4)
5.2.1 General Solution
64(1)
5.2.2 Example: Gaussian Distribution
65(2)
5.3 General Potentials
67(2)
5.4 Exercises
69(4)
6 Interaction-Free Measurement
73(14)
6.1 Experimental Results
73(5)
6.1.1 Classical Light Rays and Particles in the Mach-Zehnder Interferometer
73(3)
6.1.2 Photons in the Mach-Zehnder Interferometer
76(2)
6.2 Formal Description, Unitary Operators
78(4)
6.2.1 First Approach
79(1)
6.2.2 Second Approach (Operators)
80(2)
6.3 Concluding Remarks
82(3)
6.3.1 Extensions
82(1)
6.3.2 Quantum Zeno Effect
83(1)
6.3.3 Delayed-Choice Experiments
83(1)
6.3.4 The Hadamard Transformation
84(1)
6.3.5 From the MZI to the Quantum Computer
84(1)
6.3.6 Hardy's Experiment
84(1)
6.3.7 How Interaction-Free is the `Interaction-Free' Quantum Measurement?
84(1)
6.4 Exercises
85(2)
7 Position Probability
87(14)
7.1 Position Probability and Measurements
88(6)
7.1.1 Example: Infinite Potential Wall
88(1)
7.1.2 Bound Systems
89(3)
7.1.3 Free Systems
92(2)
7.2 Real Potentials
94(2)
7.3 Probability Current Density
96(2)
7.4 Exercises
98(3)
8 Neutrino Oscillations
101(10)
8.1 The Neutrino Problem
101(1)
8.2 Modelling the Neutrino Oscillations
102(4)
8.2.1 States
102(1)
8.2.2 Time Evolution
103(1)
8.2.3 Numerical Data
104(1)
8.2.4 Three-Dimensional Neutrino Oscillations
105(1)
8.3 Generalizations
106(3)
8.3.1 Hermitian Operators
106(2)
8.3.2 Time Evolution and Measurement
108(1)
8.4 Exercises
109(2)
9 Expectation Values, Mean Values, and Measured Values
111(16)
9.1 Mean Values and Expectation Values
111(7)
9.1.1 Mean Values of Classical Measurements
111(1)
9.1.2 Expectation Value of the Position in Quantum Mechanics
112(1)
9.1.3 Expectation Value of the Momentum in Quantum Mechanics
113(2)
9.1.4 General Definition of the Expectation Value
115(2)
9.1.5 Variance, Standard Deviation
117(1)
9.2 Hermitian Operators
118(3)
9.2.1 Hermitian Operators Have Real Eigenvalues
119(1)
9.2.2 Eigenfunctions of Different Eigenvalues Are Orthogonal
120(1)
9.3 Time Behavior, Conserved Quantities
121(3)
9.3.1 Time Behavior of Expectation Values
121(1)
9.3.2 Conserved Quantities
122(1)
9.3.3 Ehrenfest's Theorem
123(1)
9.4 Exercises
124(3)
10 Stopover; then on to Quantum Cryptography
127(14)
10.1 Outline
127(1)
10.2 Summary and Open Questions
127(5)
10.2.1 Summary
128(3)
10.2.2 Open Questions
131(1)
10.3 Quantum Cryptography
132(9)
10.3.1 Introduction
133(1)
10.3.2 One-time Pad
133(2)
10.3.3 BB84 Protocol Without Eve
135(2)
10.3.4 BB84 Protocol with Eve
137(4)
11 Abstract Notation
141(12)
11.1 Hilbert Space
141(4)
11.1.1 Wavefunctions and Coordinate Vectors
141(2)
11.1.2 The Scalar Product
143(1)
11.1.3 Hilbert Space
144(1)
11.2 Matrix Mechanics
145(1)
11.3 Abstract Formulation
146(4)
11.4 Concrete: Abstract
150(2)
11.5 Exercises
152(1)
12 Continuous Spectra
153(14)
12.1 Improper Vectors
154(5)
12.2 Position Representation and Momentum Representation
159(4)
12.3 Conclusions
163(1)
12.4 Exercises
164(3)
13 Operators
167(22)
13.1 Hermitian Operators, Observables
168(8)
13.1.1 Three Important Properties of Hermitian Operators
169(3)
13.1.2 Uncertainty Relations
172(3)
13.1.3 Degenerate Spectra
175(1)
13.2 Unitary Operators
176(3)
13.2.1 Unitary Transformations
176(1)
13.2.2 Functions of Operators, the Time-Evolution Operator
177(2)
13.3 Projection Operators
179(4)
13.3.1 Spectral Representation
180(1)
13.3.2 Projection and Properties
181(1)
13.3.3 Measurements
182(1)
13.4 Systematics of the Operators
183(1)
13.5 Exercises
184(5)
14 Postulates of Quantum Mechanics
189(16)
14.1 Postulates
190(6)
14.1.1 States, State Space (Question 1)
190(2)
14.1.2 Probability Amplitudes, Probability (Question 2)
192(1)
14.1.3 Physical Quantities and Hermitian Operators (Question 2)
192(1)
14.1.4 Measurement and State Reduction (Question 2)
193(1)
14.1.5 Time Evolution (Question 3)
194(2)
14.2 Some Open Problems
196(5)
14.3 Concluding Remarks
201(1)
14.3.1 Postulates of Quantum Mechanics as a Framework
201(1)
14.3.2 Outlook
201(1)
14.4 Exercises
202(3)
Appendix A Abbreviations and Notations 205(2)
Appendix B Units and Constants 207(6)
Appendix C Complex Numbers 213(10)
Appendix D Calculus I 223(16)
Appendix E Calculus II 239(8)
Appendix F Linear Algebra I 247(18)
Appendix G Linear Algebra II 265(10)
Appendix H Fourier Transforms and the Delta Function 275(18)
Appendix I Operators 293(20)
Appendix J From Quantum Hopping to the Schrodinger Equation 313(6)
Appendix K The Phase Shift at a Beam Splitter 319(2)
Appendix L The Quantum Zeno Effect 321(8)
Appendix M Delayed Choice and the Quantum Eraser 329(6)
Appendix N The Equation of Continuity 335(2)
Appendix O Variance, Expectation Values 337
Jochen Pade studied physics in Freiburg (Germany), where he received his PhD in theoretical physics in 1978. Since 1980, he has been a lecturer at the Carl von Ossietzky University Oldenburg (Germany). His research interests are: Theoretical physics, didactics and popularisation of science.