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El. knyga: Quantum Mechanics II: Advanced Topics

(Bharathidasan University, Tiruchirapalli, India), (ANJA College, Tamilnadu, India)
  • Formatas: 432 pages
  • Išleidimo metai: 24-Nov-2022
  • Leidėjas: CRC Press
  • Kalba: eng
  • ISBN-13: 9781000773613
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Quantum Mechanics II: Advanced TopicsDidesnis paveikslėlis
  • Formatas: 432 pages
  • Išleidimo metai: 24-Nov-2022
  • Leidėjas: CRC Press
  • Kalba: eng
  • ISBN-13: 9781000773613
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Quantum Mechanics II: Advanced Topics offers a comprehensive exploration of the state-of-the-art in various advanced topics of current research interest. A follow-up to the authors introductory book Quantum Mechanics I: The Fundamentals, this book expounds basic principles, theoretical treatment, case studies, worked-out examples and applications of advanced topics including quantum technologies.

A thoroughly revised and updated this unique volume presents an in-depth and up-to-date progress on the growing topics including latest achievements on quantum technology. In the second edition six new chapters are included and the other ten chapters are extensively revised.

Features











Covers classical and quantum field theories, path integral formalism and supersymmetric quantum mechanics.











Highlights coherent and squeezed states, Berrys phase, AharonovBohm effect and Wigner function.











Explores salient features of quantum entanglement and quantum cryptography.





Presents basic concepts of quantum computers and the features of no-cloning theorem and quantum cloning machines.











Describes the theory and techniques of quantum tomography, quantum simulation and quantum error correction.











Introduces other novel topics including quantum versions of theory of gravity, cosmology, Zeno effect, teleportation, games, chaos and steering.











Outlines the quantum technologies of ghost imaging, detection of weak amplitudes and displacements, lithography, metrology, teleportation of optical images, sensors, batteries and internet.











Contains several worked-out problems and exercises in each chapter.

Quantum Mechanics II: Advanced Topics addresses various currently emerging exciting topics of quantum mechanics. It emphasizes the fundamentals behind the latest cutting-edge developments to help explain the motivation for deeper exploration. The book is a valuable resource for graduate students in physics and engineering wishing to pursue research in quantum mechanics.
Preface xiii
About the Authors xvii
1 Quantum Field Theory
1(32)
1.1 Introduction
1(1)
1.2 Why Quantum Field Theory?
1(1)
1.3 What is a Field?
2(1)
1.4 Classical Field Theory
3(4)
1.5 Quantum Equations for Fields
7(1)
1.6 Quantization of Nonrelativistic Wave Equation
8(4)
1.7 Electromagnetic Field in Vacuum
12(5)
1.8 Interaction of Charged Particles with Electromagnetic Field
17(3)
1.9 Quantization of Klein-Gordon Equation
20(5)
1.10 Quantization of Dirac Field
25(2)
1.11 Gauge Field Theories
27(2)
1.12 Concluding Remarks
29(1)
1.13 Bibliography
29(1)
1.14 Exercises
30(3)
2 Path Integral Formulation
33(18)
2.1 Introduction
33(1)
2.2 Time Evolution of Wave Function and Propagator
34(1)
2.3 Path Integral Representation of Propagator
35(1)
2.4 Connection Between Propagator and Classical Action
36(3)
2.5 Schrodinger Equation From Path Integral Formulation
39(1)
2.6 Transition Amplitude of a Free Particle
40(2)
2.7 Systems with Quadratic Lagrangian
42(6)
2.8 Path Integral Version of Ehrenfest's Theorem
48(1)
2.9 Concluding Remarks
48(1)
2.10 Bibliography
49(1)
2.11 Exercises
50(1)
3 Supersyrnmetric Quantum Mechanics
51(24)
3.1 Introduction
51(1)
3.2 Supersyrnmetric Potentials
52(6)
3.3 Relations Between the Eigenstates of Two Supersyrnmetric Hamiltonians
58(3)
3.4 Hierarchy of Supersyrnmetric Hamiltonians
61(1)
3.5 Applications
62(4)
3.6 Generation of Complex Potentials with Real Eigenvalues
66(5)
3.7 Concluding Remarks
71(1)
3.8 Bibliography
71(2)
3.9 Exercises
73(2)
4 Coherent and Squeezed States
75(30)
4.1 Introduction
75(1)
4.2 The Uncertainty Product of Harmonic Oscillator
76(2)
4.3 Coherent States: Definition, Uncertainty Product and Physical Meaning
78(2)
4.4 Generation and Properties of Coherent States
80(6)
4.5 Spin Coherent States
86(1)
4.6 Coherent States of Position-Dependent Mass Systems
87(2)
4.7 Squeezed States
89(5)
4.8 Deformed Oscillators and Nonlinear Coherent States
94(4)
4.9 Concluding Remarks
98(1)
4.10 Bibliography
98(4)
4.11 Exercises
102(3)
5 Berry's Phase, Aharonov-Bohm and Sagnac Effects
105(26)
5.1 Introduction
105(1)
5.2 Derivation of Berry's Phase
106(2)
5.3 Origin and Properties of Berry's Phase
108(1)
5.4 Classical Analogue of Berry's Phase
109(2)
5.5 Berry's Phase in Solid State Physics
111(2)
5.6 Examples and Effects of Berry's Phase
113(1)
5.7 Applications of Berry's Phase
114(2)
5.8 Experimental Verification of Berry's Phase
116(1)
5.9 Pancharatnam's Work
117(1)
5.10 Cumulants Associated with Geometric Phases
118(1)
5.11 The Aharonov-Bohm Effect
119(4)
5.12 Sagnac Effect
123(3)
5.13 Concluding Remarks
126(1)
5.14 Bibliography
127(2)
5.15 Exercises
129(2)
6 Phase Space Picture and Canonical Transformations
131(20)
6.1 Introduction
131(1)
6.2 Squeeze and Rotation in Phase Space
132(2)
6.3 Linear Canonical Transformations
134(1)
6.4 Wigner Function
135(4)
6.5 Time Evolution of the Wigner Function
139(3)
6.6 Applications
142(4)
6.7 Advantages of the Wigner Function
146(1)
6.8 Concluding Remarks
147(1)
6.9 Bibliography
147(2)
6.10 Exercises
149(2)
7 Quantum Entanglement
151(28)
7.1 Introduction
151(1)
7.2 States in Classical Mechanics
152(1)
7.3 Quantum Entangled States
153(3)
7.4 Mixed States
156(2)
7.5 Bipartite Systems
158(3)
7.6 Separability Criteria
161(4)
7.7 Multipartite Entanglement
165(1)
7.8 Quantifying Entanglement
166(5)
7.9 Applications of Entanglement
171(2)
7.10 Concluding Remarks
173(1)
7.11 Bibliography
174(3)
7.12 Exercises
177(2)
8 Quantum Decoherence
179(22)
8.1 Introduction
179(1)
8.2 Decoherence and Interference Damping
180(1)
8.3 Interaction of a Detector on the Double-Slit Experiment
181(1)
8.4 Decoherence Due to Phase Randomization
182(3)
8.5 Position Decoherence Due to Environmental Scattering
185(2)
8.6 Master Equations
187(4)
8.7 Decoherence Models
191(1)
8.8 Decoherence Experiments
192(3)
8.9 The Role of Decoherence in the Interpretation of Quantum Mechanics
195(3)
8.10 Concluding Remarks
198(1)
8.11 Bibliography
198(2)
8.12 Exercises
200(1)
9 Quantum Computers
201(28)
9.1 Introduction
201(1)
9.2 What is a Quantum Computer?
201(3)
9.3 Why is a Quantum Computer?
204(1)
9.4 Fundamental Properties
205(8)
9.5 Quantum Algorithms
213(7)
9.6 Testing Quantum Computers Using Grover's Algorithm
220(1)
9.7 Features of Quantum Computation
221(1)
9.8 Quantum Computation Through NMR
221(1)
9.9 Why is Making a Quantum Computer Extremely Difficult?
222(1)
9.10 Concluding Remarks
223(1)
9.11 Bibliography
223(2)
9.12 Exercises
225(4)
10 Quantum Cryptography
229(22)
10.1 Introduction
229(1)
10.2 Standard Cryptosystems
229(2)
10.3 Quantum Cryptography-Basic Principle
231(2)
10.4 Types of Quantum Cryptography
233(6)
10.5 Multiparty Quantum Secret Sharing
239(2)
10.6 Applications of Quantum Cryptography
241(1)
10.7 Implementation and Limitations
242(1)
10.8 Fiber-Optical Quantum Key Distribution
243(1)
10.9 Quantum Cheque Scheme
243(3)
10.10 Concluding Remarks
246(1)
10.11 Bibliography
247(1)
10.12 Exercises
248(3)
11 No-Cloning Theorem and Quantum Cloning Machines
251(16)
11.1 Introduction
251(1)
11.2 Proof of No-Cloning Theorem
251(2)
11.3 No-Broadcasting Theorem
253(2)
11.4 No-Cloning and No-Superluminar Signalling
255(1)
11.5 Quantum Cloning Machines
256(5)
11.6 Quantum Telecloning
261(2)
11.7 Other No-Go Theorems
263(1)
11.8 Concluding Remarks
264(1)
11.9 Bibliography
264(1)
11.10 Exercises
265(2)
12 Quantum Tomography
267(20)
12.1 Introduction
267(1)
12.2 Pauli Problem
268(2)
12.3 Recovery of Density Matrix from Wigner Function
270(3)
12.4 Optical Homodyne Tomography
273(1)
12.5 Qubit Quantum Tomography
274(3)
12.6 Experimental Measure of Polarization of a Photonic Qubit
277(2)
12.7 Multiqubit Tomography
279(1)
12.8 Quantum Process Tomography
280(3)
12.9 Conclusion
283(1)
12.10 Bibliography
283(2)
12.11 Exercises
285(2)
13 Quantum Simulation
287(18)
13.1 Introduction
287(1)
13.2 Limitations of Classical Computers in Simulating Quantum Systems
288(1)
13.3 Quantum Simulators
289(1)
13.4 Analog Quantum Simulators
290(1)
13.5 Digital Quantum Simulators
291(2)
13.6 Theory of Quantum Simulation of the Schrodinger Equation
293(1)
13.7 Quantum Simulators Using Quantum Computers
294(1)
13.8 Quantum Circuits
295(4)
13.9 Quantum Circuits for Final Measurements
299(1)
13.10 Concluding Remarks
300(1)
13.11 Bibliography
300(2)
13.12 Exercises
302(3)
14 Quantum Error Correction
305(22)
14.1 Introduction
305(1)
14.2 Sources of Errors in Quantum Information Processing
305(3)
14.3 Difficulties of Using Classical Error Correction Techniques to QEC
308(2)
14.4 Digitization of Quantum Errors
310(1)
14.5 QEC Mechanisms Using Quantum Redundancy
310(4)
14.6 QEC with Stabilizer Codes
314(3)
14.7 The Surface Code
317(2)
14.8 Practical Issues in the Implementation of QEC Codes
319(3)
14.9 Concluding Remarks
322(1)
14.10 Bibliography
322(2)
14.11 Exercises
324(3)
15 Some Other Advanced Topics
327(48)
15.1 Introduction
327(1)
15.2 Quantum Theory of Gravity
327(4)
15.3 Quantum Cosmology
331(6)
15.4 Quantum Zeno Effect
337(6)
15.5 Quantum Teleportation
343(3)
15.6 Quantum Games
346(6)
15.7 Quantum Pseudo-Telepathy Games
352(6)
15.8 Quantum Steering
358(1)
15.9 Quantum Diffusion
359(3)
15.10 Quantum Chaos
362(4)
15.11 Concluding Remarks
366(1)
15.12 Bibliography
367(7)
15.13 Exercises
374(1)
16 Quantum Technologies
375(32)
16.1 Introduction
375(1)
16.2 Quantum Entangled Photons
376(2)
16.3 Ghost Imaging
378(1)
16.4 Detection of Weak Amplitude Object
379(2)
16.5 Entangled Two-Photon Microscopy
381(1)
16.6 Detection of Small Displacements
382(2)
16.7 Quantum Lithography
384(2)
16.8 Quantum Metrology
386(3)
16.9 Quantum Teleportation of Optical Images
389(1)
16.10 Quantum Sensors
389(5)
16.11 Quantum Batteries
394(3)
16.12 Quantum Internet
397(2)
16.13 Concluding Remarks
399(1)
16.14 Bibliography
400(6)
16.15 Exercises
406(1)
Solutions to Selected Exercises 407(4)
Index 411
S. Rajasekar received his B.Sc.and M.Sc. in Physics both from St. Josephs College, Tiruchirapalli. He was awarded his Ph.D. degree from Bharathidasan University in 1992 under the supervision of Prof. M. Lakshmanan. In 1993, he joined as a Lecturer at the Department of Physics, Manonmaniam Sundaranar University, Tirunelveli. In 2003, the book Nonlinear Dynamics: Integrability, Chaos and Patterns written by Prof. M. Lakshmanan and the author was published by Springer. In 2005, he joined as a Professor at the School of Physics, Bharathidasan University. In 2016 Springer published Nonlinear Resonances written by Prof. Miguel A.F. Sanjuan and the author. In 2021 Professors U.E. Vincent, P.V.E. McClintock, I.A. Khovanov and the author compiled and edited two issues of Philosophical Transactions of the Royal Society A on the theme Vibrational and Stochastic Resonances in Driven Nonlinear Systems. He has also edited Recent Trends in Chaotic, Nonlinear and Complex Dynamics with Professors Jan Awrejecewicz and Minvydas Ragulskis, published by World Scientic in 2022. His recent research focuses on nonlinear dynamics with a special emphasize on nonlinear resonances. He has authored or co-authored more than 120 research papers in nonlinear dynamics.

R. Velusamy received his B.Sc. degree in Physics from the Ayya Nadar Janaki Am-mal College, Sivakasi in 1972 and M.Sc. in Physics from the P.S.G. Arts and Science College, Coimbatore in 1974. He worked as a demonstrator in the Department of Physics in P.S.G. Arts and Science College during 1974-77. He received an M.S. Degree in Electrical Engineering at Indian Institute of Technology, Chennai in the year 1981. In the same year, he joined in the Ayya Nadar Janaki Ammal College as an Assistant Professor in Physics. He was awarded a M.Phil. degree in Physics in the year 1988. He retired in the year 2010. His research topics are quantum conned systems and wave packet dynamics.
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