Quantum Mechanics II: Advanced Topics

✍ Scribed by S. Rajasekar, R. Velusamy

• Publisher: CRC Press
• Year: 2022
• Tongue: English
• Leaves: 433
• Edition: 2
• Category: Library

✦ Synopsis

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, Berry’s phase, Aharonov―Bohm 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.

✦ Table of Contents

Cover
Half Title
Title Page
Copyright Page
Dedication
Contents
Preface
About the Authors
1. Quantum Field Theory
1.1. Introduction
1.2. Why Quantum Field Theory?
1.3. What is a Field?
1.4. Classical Field Theory
1.5. Quantum Equations for Fields
1.6. Quantization of Nonrelativistic Wave Equation
1.7. Electromagnetic Field in Vacuum
1.8. Interaction of Charged Particles with Electromagnetic Field
1.9. Quantization of Klein–Gordon Equation
1.10. Quantization of Dirac Field
1.11. Gauge Field Theories
1.12. Concluding Remarks
1.13. Bibliography
1.14. Exercises
2. Path Integral Formulation
2.1. Introduction
2.2. Time Evolution of Wave Function and Propagator
2.3. Path Integral Representation of Propagator
2.4. Connection Between Propagator and Classical Action
2.5. Schrodinger Equation From Path Integral Formulation
2.6. Transition Amplitude of a Free Particle
2.7. Systems with Quadratic Lagrangian
2.8. Path Integral Version of Ehrenfest's Theorem
2.9. Concluding Remarks
2.10. Bibliography
2.11. Exercises
3. Supersymmetric Quantum Mechanics
3.1. Introduction
3.2. Supersymmetric Potentials
3.3. Relations Between the Eigenstates of Two Supersymmetric Hamiltonians
3.4. Hierarchy of Supersymmetric Hamiltonians
3.5. Applications
3.6. Generation of Complex Potentials with Real Eigenvalues
3.7. Concluding Remarks
3.8. Bibliography
3.9. Exercises
4. Coherent and Squeezed States
4.1. Introduction
4.2. The Uncertainty Product of Harmonic Oscillator
4.3. Coherent States: De nition, Uncertainty Product and Physical Meaning
4.4. Generation and Properties of Coherent States
4.5. Spin Coherent States
4.6. Coherent States of Position-Dependent Mass Systems
4.7. Squeezed States
4.8. Deformed Oscillators and Nonlinear Coherent States
4.9. Concluding Remarks
4.10. Bibliography
4.11. Exercises
5. Berry's Phase, Aharonov–Bohm and Sagnac Effects
5.1. Introduction
5.2. Derivation of Berry's Phase
5.3. Origin and Properties of Berry's Phase
5.4. Classical Analogue of Berry's Phase
5.5. Berry's Phase in Solid State Physics
5.6. Examples and E ects of Berry's Phase
5.7. Applications of Berry's Phase
5.8. Experimental Veri cation of Berry's Phase
5.9. Pancharatnam's Work
5.10. Cumulants Associated with Geometric Phases
5.11. The Aharonov–Bohm Effect
5.12. Sagnac Effect
5.13. Concluding Remarks
5.14. Bibliography
5.15. Exercises
6. Phase Space Picture and Canonical Transformations
6.1. Introduction
6.2. Squeeze and Rotation in Phase Space
6.3. Linear Canonical Transformations
6.4. Wigner Function
6.5. Time Evolution of the Wigner Function
6.6. Applications
6.7. Advantages of the Wigner Function
6.8. Concluding Remarks
6.9. Bibliography
6.10. Exercises
7. Quantum Entanglement
7.1. Introduction
7.2. States in Classical Mechanics
7.3. Quantum Entangled States
7.4. Mixed States
7.5. Bipartite Systems
7.6. Separability Criteria
7.7. Multipartite Entanglement
7.8. Quantifying Entanglement
7.9. Applications of Entanglement
7.10. Concluding Remarks
7.11. Bibliography
7.12. Exercises
8. Quantum Decoherence
8.1. Introduction
8.2. Decoherence and Interference Damping
8.3. Interaction of a Detector on the Double-Slit Experiment
8.4. Decoherence Due to Phase Randomization
8.5. Position Decoherence Due to Environmental Scattering
8.6. Master Equations
8.7. Decoherence Models
8.8. Decoherence Experiments
8.9. The Role of Decoherence in the Interpretation of Quantum Mechanics
8.10. Concluding Remarks
8.11. Bibliography
8.12. Exercises
9. Quantum Computers
9.1. Introduction
9.2. What is a Quantum Computer?
9.3. Why is a Quantum Computer?
9.4. Fundamental Properties
9.5. Quantum Algorithms
9.6. Testing Quantum Computers Using Grover's Algorithm
9.7. Features of Quantum Computation
9.8. Quantum Computation Through NMR
9.9. Why is Making a Quantum Computer Extremely Diffcult?
9.10. Concluding Remarks
9.11. Bibliography
9.12. Exercises
10. Quantum Cryptography
10.1. Introduction
10.2. Standard Cryptosystems
10.3. Quantum Cryptography–Basic Principle
10.4. Types of Quantum Cryptography
10.5. Multiparty Quantum Secret Sharing
10.6. Applications of Quantum Cryptography
10.7. Implementation and Limitations
10.8. Fiber-Optical Quantum Key Distribution
10.9. Quantum Cheque Scheme
10.10. Concluding Remarks
10.11. Bibliography
10.12. Exercises
11. No-Cloning Theorem and Quantum Cloning Machines
11.1. Introduction
11.2. Proof of No-Cloning Theorem
11.3. No-Broadcasting Theorem
11.4. No-Cloning and No-Superluminar Signalling
11.5. Quantum Cloning Machines
11.6. Quantum Telecloning
11.7. Other No-Go Theorems
11.8. Concluding Remarks
11.9. Bibliography
11.10. Exercises
12. Quantum Tomography
12.1. Introduction
12.2. Pauli Problem
12.3. Recovery of Density Matrix from Wigner Function
12.4. Optical Homodyne Tomography
12.5. Qubit Quantum Tomography
12.6. Experimental Measure of Polarization of a Photonic Qubit
12.7. Multiqubit Tomography
12.8. Quantum Process Tomography
12.9. Conclusion
12.10. Bibliography
12.11. Exercises
13. Quantum Simulation
13.1. Introduction
13.2. Limitations of Classical Computers in Simulating Quantum Systems
13.3. Quantum Simulators
13.4. Analog Quantum Simulators
13.5. Digital Quantum Simulators
13.6. Theory of Quantum Simulation of the Schrodinger Equation
13.7. Quantum Simulators Using Quantum Computers
13.8. Quantum Circuits
13.9. Quantum Circuits for Final Measurements
13.10. Concluding Remarks
13.11. Bibliography
13.12. Exercises
14. Quantum Error Correction
14.1. Introduction
14.2. Sources of Errors in Quantum Information Processing
14.3. Di culties of Using Classical Error Correction Techniques to QEC
14.4. Digitization of Quantum Errors
14.5. QEC Mechanisms Using Quantum Redundancy
14.6. QEC with Stabilizer Codes
14.7. The Surface Code
14.8. Practical Issues in the Implementation of QEC Codes
14.9. Concluding Remarks
14.10. Bibliography
14.11. Exercises
15. Some Other Advanced Topics
15.1. Introduction
15.2. Quantum Theory of Gravity
15.3. Quantum Cosmology
15.4. Quantum Zeno Effect
15.5. Quantum Teleportation
15.6. Quantum Games
15.7. Quantum Pseudo-Telepathy Games
15.8. Quantum Steering
15.9. Quantum Diffusion
15.10. Quantum Chaos
15.11. Concluding Remarks
15.12. Bibliography
15.13. Exercises
16. Quantum Technologies
16.1. Introduction
16.2. Quantum Entangled Photons
16.3. Ghost Imaging
16.4. Detection of Weak Amplitude Object
16.5. Entangled Two-Photon Microscopy
16.6. Detection of Small Displacements
16.7. Quantum Lithography
16.8. Quantum Metrology
16.9. Quantum Teleportation of Optical Images
16.10. Quantum Sensors
16.11. Quantum Batteries
16.12. Quantum Internet
16.13. Concluding Remarks
16.14. Bibliography
16.15. Exercises
Solutions to Selected Exercises
Index