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Quantum Mechanics for Pedestrians 2014 ed., 2, Applications and Extensions [Minkštas viršelis]

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  • Formatas: Paperback / softback, 482 pages, aukštis x plotis: 235x155 mm, weight: 765 g, 32 black & white illustrations, 49 colour illustrations, biography
  • Serija: Undergraduate Lecture Notes in Physics
  • Išleidimo metai: 08-Nov-2013
  • Leidėjas: Springer International Publishing AG
  • ISBN-10: 3319008129
  • ISBN-13: 9783319008127
Kitos knygos pagal šią temą:
Quantum Mechanics for Pedestrians 2014 ed., 2, Applications and ExtensionsDidesnis paveikslėlis
  • Formatas: Paperback / softback, 482 pages, aukštis x plotis: 235x155 mm, weight: 765 g, 32 black & white illustrations, 49 colour illustrations, biography
  • Serija: Undergraduate Lecture Notes in Physics
  • Išleidimo metai: 08-Nov-2013
  • Leidėjas: Springer International Publishing AG
  • ISBN-10: 3319008129
  • ISBN-13: 9783319008127
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9783319008127.html
Raktažodžiai:
The two-volume textbook Quantum Mechanics for Pedestrians provides an introduction to the basics of nonrelativistic quantum mechanics. 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. The basic principles of quantum mechanics are presented in the first volume. This second volume discusses applications and extensions to more complex problems. In addition to topics traditionally dealt with in quantum mechanics texts, such as symmetries or many-body problems, here also issues of current interest such as entanglement, Bell's inequalities, decoherence and various aspects of quantum information are treated in detail. Furthermore, questions of the basis of quantum mechanics and epistemological issues are discussed explicitly; these are relevant e.g. to the realism debate. A chapter on the interpretations of quantum mechanics completes this volume. The necessary mathematical tools are introduced step by step; in the appendix, the most relevant mathematics is compiled in compact form. More advanced topics such as the Lenz vector, Hardy's experiment and Shor's algorithm are treated in more detail in the appendix. As an essential aid to learning and teaching, 130 exercises are included, most of them with their solutions.

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.
Introduction xvii
Overview of Volume 2 xxi
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 < 0
12(3)
15.3.2 Potential Well, E > 0
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
68(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
71(2)
19.3.2 Results of Perturbation Theory
73(1)
19.3.3 Comparison with the Results of the Dirac Equation
74(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
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(16)
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(4)
23.4.1 Spectrum Without V1,2
138(2)
23.4.2 Spectrum with V1,2 (Perturbation Theory)
140(2)
23.5 The Ritz Method
142(2)
23.6 How Far does the Pauli Principle Reach?
144(2)
23.6.1 Distinguishable Quantum Objects
144(1)
23.6.2 Identical Quantum Objects
145(1)
23.7 Exercises
146(1)
24 Decoherence
147(20)
24.1 A Simple Example
148(2)
24.2 Decoherence
150(9)
24.2.1 The Effect of the Environment I
152(2)
24.2.2 Simplified Description
154(1)
24.2.3 The Effect of the Environment II
155(2)
24.2.4 Interim Review
157(1)
24.2.5 Formal Treatment
158(1)
24.3 Time Scales, Universality
159(1)
24.4 Decoherence-Free Subspaces, Basis
160(1)
24.5 Historical Side Note
161(1)
24.6 Conclusions
162(2)
24.7 Exercises
164(3)
25 Scattering
167(14)
25.1 Basic Idea; Scattering Cross Section
168(3)
25.1.1 Classical Mechanics
168(1)
25.1.2 Quantum Mechanics
169(2)
25.2 The Partial-Wave Method
171(4)
25.3 Integral Equations, Born Approximation
175(3)
25.4 Exercises
178(3)
26 Quantum Information
181(20)
26.1 No-Cloning Theorem (Quantum Copier)
181(2)
26.2 Quantum Cryptography
183(1)
26.3 Quantum Teleportation
183(3)
26.4 The Quantum Computer
186(12)
26.4.1 Qubits, Registers (Basic Concepts)
186(2)
26.4.2 Quantum Gates and Quantum Computers
188(4)
26.4.3 The Basic Idea of the Quantum Computer
192(1)
26.4.4 The Deutsch Algorithm
193(1)
26.4.5 Grover's Search Algorithm
194(2)
26.4.6 Shor's Algorithm
196(1)
26.4.7 On The Construction of Real Quantum Computers
197(1)
26.5 Exercises
198(3)
27 Is Quantum Mechanics Complete?
201(16)
27.1 The Kochen---Specker Theorem
202(6)
27.1.1 Value Function
203(1)
27.1.2 From the Value Function to Coloring
204(1)
27.1.3 Coloring
205(2)
27.1.4 Interim Review: The Kochen-Specker Theorem
207(1)
27.2 GHZ States
208(3)
27.3 Discussion and Outlook
211(3)
27.4 Exercises
214(3)
28 Interpretations of Quantum Mechanics
217(16)
28.1 Preliminary Remarks
219(4)
28.1.1 Problematic Issues
219(3)
28.1.2 Difficulties in the Representation of Interpretations
222(1)
28.2 Some Interpretations in Short Form
223(7)
28.2.1 Copenhagen Interpretation(s)
223(2)
28.2.2 Ensemble Interpretation
225(1)
28.2.3 Bohm's Interpretation
226(1)
28.2.4 Many-Worlds Interpretation
227(1)
28.2.5 Consistent-Histories Interpretation
228(1)
28.2.6 Collapse Theories
228(1)
28.2.7 Other Interpretations
229(1)
28.3 Conclusion
230(3)
Appendix A Abbreviations and Notations 233(4)
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(6)
Appendix G The Lenz Vector 273(14)
Appendix H Perturbative Calculation of the Hydrogen Atom 287(4)
Appendix I The Production of Entangled Photons 291(4)
Appendix J The Hardy Experiment 295(8)
Appendix K Set-Theoretical Derivation of the Bell Inequality 303(2)
Appendix L The Special Galilei Transformation 305(12)
Appendix M Kramers' Theorem 317(2)
Appendix N Coulomb Energy and Exchange Energy in the Helium Atom 319(4)
Appendix O The Scattering of Identical Particles 323(4)
Appendix P The Hadamard Transformation 327(4)
Appendix Q From the Interferometer to the Computer 331(6)
Appendix R The Grover Algorithm, Algebraically 337(6)
Appendix S Shor Algorithm 343(16)
Appendix T The Gleason Theorem 359
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.