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El. knyga: Quantum Mechanics for Pedestrians 2: Applications and Extensions

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This book, the second in a two-volume set, provides an introduction to the basics of (mainly) non-relativistic quantum mechanics. While the first volume addresses the basic principles, this second volume discusses applications and extensions to more complex problems. In addition to topics dealt with in traditional quantum mechanics texts, such as symmetries or many-body problems, it also treats issues of current interest such as entanglement, Bell’s inequality, decoherence and various aspects of quantum information in detail. Furthermore, questions concerning the basis of quantum mechanics and epistemological issues which are relevant e.g. to the realism debate are discussed explicitly. A chapter on the interpretations of quantum mechanics rounds out the book.

Readers are introduced to the requisite mathematical tools step by step. In the appendix, the most relevant mathematics is compiled in compact form, and more advanced topics such as the Lenz vector, Hardy’s experiment and Shor’s algorithm are treated in more detail. As an essential aid to learning and teaching, 130 exercises are included, most of them with solutions.

This revised second edition is expanded by an introduction into some ideas and problems of relativistic quantum mechanics. In this second volume, an overview of quantum field theory is given and basic conceptions of quantum electrodynamics are treated in some detail.

Originally written as a course for students of science education, the book addresses all those science students and others who are looking for a reasonably simple, fresh and modern introduction to the field.



This book provides an introduction into the fundamentals of non-relativistic quantum mechanics. The second of a two-volume reference, it discusses applications and extensions to more complex problems. Includes exercises and problems with solutions.

Recenzijos

This book continues the excellent introduction to quantum mechanics of the first volume ... suited for beginners to get first insights which may be deepened reading the appendices. The two volumes can be best recommended generally and especially for self studies. (K.-E. Hellwig, zbMATH 1445.81002, 2020)

Part II Applications and Extensions
15 One-Dimensional Piecewise-Constant Potentials
3(26)
15.1 General Remarks
4(2)
15.2 Potential Steps
6(5)
15.2.1 Potential Step, E > V0
7(1)
15.2.2 Potential Step, E < V0
8(3)
15.3 Finite Potential Well
11(6)
15.3.1 Potential Well, E > V0
12(3)
15.3.2 Potential Well, E < V0
15(2)
15.4 Potential Barrier, Tunnel Effect
17(3)
15.5 From the Finite to the Infinite Potential Well
20(2)
15.6 Wave Packets
22(3)
15.7 Exercises
25(4)
16 Angular Momentum
29(14)
16.1 Orbital Angular Momentum Operator
29(1)
16.2 Generalized Angular Momentum, Spectrum
30(4)
16.3 Matrix Representation of Angular Momentum Operators
34(1)
16.4 Orbital Angular Momentum: Spatial Representation of the Eigenfunctions
35(2)
16.5 Addition of Angular Momenta
37(3)
16.6 Exercises
40(3)
17 The Hydrogen Atom
43(12)
17.1 Central Potential
44(3)
17.2 The Hydrogen Atom
47(5)
17.3 Complete System of Commuting Observables
52(1)
17.4 On Modelling
53(1)
17.5 Exercises
54(1)
18 The Harmonic Oscillator
55(10)
18.1 Algebraic Approach
56(5)
18.1.1 Creation and Annihilation Operators
56(2)
18.1.2 Properties of the Occupation-Number Operator
58(1)
18.1.3 Derivation of the Spectrum
58(3)
18.1.4 Spectrum of the Harmonic Oscillator
61(1)
18.2 Analytic Approach (Position Representation)
61(2)
18.3 Exercises
63(2)
19 Perturbation Theory
65(14)
19.1 Stationary Perturbation Theory, Nondegenerate
66(3)
19.1.1 Calculation of the First-Order Energy Correction
67(1)
19.1.2 Calculation of the First-Order State Correction
68(1)
19.2 Stationary Perturbation Theory, Degenerate
69(1)
19.3 Hydrogen: Fine Structure
70(4)
19.3.1 Relativistic Corrections to the Hamiltonian
70(2)
19.3.2 Results of Perturbation Theory
72(1)
19.3.3 Comparison with the Results of the Dirac Equation
73(1)
19.4 Hydrogen: Lamb Shift and Hyperfine Structure
74(2)
19.5 Exercises
76(3)
20 Entanglement, EPR, Bell
79(20)
20.1 Product Space N
79(1)
20.2 Entangled States
80(8)
20.2.1 Definition
81(2)
20.2.2 Single Measurements on Entangled States
83(2)
20.2.3 Schrodinger's Cat
85(2)
20.2.4 A Misunderstanding
87(1)
20.3 The EPR Paradox
88(3)
20.4 Bell's Inequality
91(5)
20.4.1 Derivation of Bell's Inequality
91(1)
20.4.2 EPR Photon Pairs
92(1)
20.4.3 EPR and Bell
93(3)
20.5 Conclusions
96(1)
20.6 Exercises
97(2)
21 Symmetries and Conservation Laws
99(18)
21.1 Continuous Symmetry Transformations
101(8)
21.1.1 General: Symmetries and Conservation Laws
101(2)
21.1.2 Time Translation
103(1)
21.1.3 Spatial Translation
104(2)
21.1.4 Spatial Rotation
106(3)
21.1.5 Special Galilean Transformation
109(1)
21.2 Discrete Symmetry Transformations
109(5)
21.2.1 Parity
109(2)
21.2.2 Time Reversal
111(3)
21.3 Exercises
114(3)
22 The Density Operator
117(14)
22.1 Pure States
117(3)
22.2 Mixed States
120(3)
22.3 Reduced Density Operator
123(5)
22.3.1 Example
125(1)
22.3.2 Comparison
126(1)
22.3.3 General Formulation
127(1)
22.4 Exercises
128(3)
23 Identical Particles
131(18)
23.1 Distinguishable Particles
132(1)
23.2 Identical Particles
133(4)
23.2.1 A Simple Example
133(1)
23.2.2 The General Case
134(3)
23.3 The Pauli Exclusion Principle
137(1)
23.4 The Helium Atom
138(5)
23.4.1 Spectrum Without V1, 2
139(2)
23.4.2 Spectrum with V1, 2 (Perturbation Theory)
141(2)
23.5 The Ritz Method
143(2)
23.6 How Far does the Pauli Principle Reach?
145(2)
23.6.1 Distinguishable Quantum Objects
146(1)
23.6.2 Identical Quantum Objects
146(1)
23.7 Exercises
147(2)
24 Decoherence
149(20)
24.1 A Simple Example
150(2)
24.2 Decoherence
152(9)
24.2.1 The Effect of the Environment I
154(2)
24.2.2 Simplified Description
156(1)
24.2.3 The Effect of the Environment II
157(2)
24.2.4 Interim Review
159(1)
24.2.5 Formal Treatment
160(1)
24.3 Time Scales, Universality
161(1)
24.4 Decoherence-Free Subspaces, Basis
162(1)
24.5 Historical Side Note
163(1)
24.6 Conclusions
164(2)
24.7 Exercises
166(3)
25 Scattering
169(14)
25.1 Basic Idea; Scattering Cross Section
170(3)
25.1.1 Classical Mechanics
170(1)
25.1.2 Quantum Mechanics
171(2)
25.2 The Partial-Wave Method
173(4)
25.3 Integral Equations, Born Approximation
177(3)
25.4 Exercises
180(3)
26 Quantum Information
183(20)
26.1 No-Cloning Theorem (Quantum Copier)
183(2)
26.2 Quantum Cryptography
185(1)
26.3 Quantum Teleportation
185(3)
26.4 The Quantum Computer
188(13)
26.4.1 Qubits, Registers (Basic Concepts)
188(2)
26.4.2 Quantum Gates and Quantum Computers
190(4)
26.4.3 The Basic Idea of the Quantum Computer
194(1)
26.4.4 The Deutsch Algorithm
194(2)
26.4.5 Grover's Search Algorithm
196(2)
26.4.6 Shor's Algorithm
198(1)
26.4.7 On The Construction of Real Quantum Computers
199(2)
26.5 Exercises
201(2)
27 Is Quantum Mechanics Complete?
203(16)
27.1 The Kochen--Specker Theorem
204(6)
27.1.1 Value Function
205(1)
27.1.2 From the Value Function to Coloring
206(1)
27.1.3 Coloring
207(2)
27.1.4 Interim Review: The Kochen-Specker Theorem
209(1)
27.2 GHZ States
210(4)
27.3 Discussion and Outlook
214(2)
27.4 Exercises
216(3)
28 Interpretations of Quantum Mechanics
219(16)
28.1 Preliminary Remarks
221(4)
28.1.1 Problematic Issues
221(3)
28.1.2 Difficulties in the Representation of Interpretations
224(1)
28.2 Some Interpretations in Short Form
225(7)
28.2.1 Copenhagen Interpretation(s)
225(2)
28.2.2 Ensemble Interpretation
227(1)
28.2.3 Bohm's Interpretation
228(1)
28.2.4 Many-Worlds Interpretation
228(2)
28.2.5 Consistent-Histories Interpretation
230(1)
28.2.6 Collapse Theories
230(1)
28.2.7 Other Interpretations
231(1)
28.3 Conclusion
232(3)
Appendix A Abbreviations and Notations 235(2)
Appendix B Special Functions 237(10)
Appendix C Tensor Product 247(6)
Appendix D Wave Packets 253(10)
Appendix E Laboratory System, Center-of-Mass System 263(4)
Appendix F Analytic Treatment of the Hydrogen Atom 267(12)
Appendix G The Lenz Vector 279(14)
Appendix H Perturbative Calculation of the Hydrogen Atom 293(4)
Appendix I The Production of Entangled Photons 297(4)
Appendix J The Hardy Experiment 301(8)
Appendix K Set-Theoretical Derivation of the Bell Inequality 309(2)
Appendix L The Special Galilei Transformation 311(12)
Appendix M Kramers' Theorem 323(2)
Appendix N Coulomb Energy and Exchange Energy in the Helium Atom 325(4)
Appendix O The Scattering of Identical Particles 329(4)
Appendix P The Hadamard Transformation 333(6)
Appendix Q From the Interferometer to the Computer 339(6)
Appendix R The Grover Algorithm, Algebraically 345(6)
Appendix S Shor Algorithm 351(16)
Appendix T The Gleason Theorem 367(2)
Appendix U What is Real? Some Quotations 369(6)
Appendix V Remarks on Some Interpretations of Quantum Mechanics 375(12)
Appendix W Elements of Quantum Field Theory 387(1)
W.1 Foreword 387(1)
W.2 Quantizing a Field - A Toy Example 388(8)
W.3 Quantization of Free Fields, Introduction 396(1)
W.4 Quantization of Free Fields, Klein-Gordon 397(8)
W.5 Quantization of Free Fields, Dirac 405(13)
W.6 Quantization of Free Fields, Photons 418(5)
W.7 Operator Ordering 423(8)
W.8 Interacting Fields, Quantum Electrodynamics 431(5)
W.9 S-Matrix, First Order 436(11)
W.10 Contraction, Propagator, Wick's Theorem 447(11)
W.11 S-Matrix,
2. Order, General		 458(4)
W.12 S-Matrix,
2. Order, 4 Lepton Scattering		 462(14)
W.13 High Precision and Infinities 476(9)
Appendix X Exercises and Solutions 485(92)
Further Reading 577(2)
Index of Volume 1 579(4)
Index of Volume 2 583
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 of Oldenburg, Germany. His main research interests are in theoretical physics, the didactics and popularization of science.
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