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## Book Description

An accessible introduction to advanced quantum theory, this graduate-level textbook focuses on its practical applications rather than mathematical technicalities. It treats real-life examples, from topics ranging from quantum transport to nanotechnology, to equip students with a toolbox of theoretical techniques. Beginning with second quantization, the authors illustrate its use with different condensed matter physics examples. They then explain how to quantize classical fields, with a focus on the electromagnetic field, taking students from Maxwell's equations to photons, coherent states and absorption and emission of photons. Following this is a unique master-level presentation on dissipative quantum mechanics, before the textbook concludes with a short introduction to relativistic quantum mechanics, covering the Dirac equation and a relativistic second quantization formalism. The textbook includes 70 end-of-chapter problems. Solutions to some problems are given at the end of the chapter and full solutions to all problems are available for instructors at www.cambridge.org/9780521761505.

1. Coverpage
3. Title page
5. Contents
6. Figure Credits
7. Preface
8. Part I Second Quantization
1. 1 Elementary quantum mechanics
1. 1.1 Classical mechanics
2. 1.2 Schrödinger equation
3. 1.3 Dirac formulation
4. 1.4 Schrödinger and Heisenberg pictures
5. 1.5 Perturbation theory
6. 1.6 Time-dependent perturbation theory
7. 1.7 Spin and angular momentum
8. 1.8 Two-level system: The qubit
9. 1.9 Harmonic oscillator
10. 1.10 The density matrix
11. 1.11 Entanglement
12. Exercises
13. Solutions
2. 2 Identical particles
1. 2.1 Schrödinger equation for identical particles
2. 2.2 The symmetry postulate
3. 2.3 Solutions of the N-particle Schrödinger equation
4. Exercises
5. Solutions
3. 3 Second quantization
1. 3.1 Second quantization for bosons
2. 3.2 Field operators for bosons
3. 3.3 Why second quantization?
4. 3.4 Second quantization for fermions
5. 3.5 Summary of second quantization
6. Exercises
7. Solutions
9. Part II Examples
1. 4 Magnetism
1. 4.1 Non-interacting Fermi gas
2. 4.2 Magnetic ground state
3. 4.3 Energy
4. 4.4 Broken symmetry
5. 4.5 Excitations in ferromagnetic metals
6. Exercises
7. Solutions
2. 5 Superconductivity
1. 5.1 Attractive interaction and Cooper pairs
2. 5.2 Energy
3. 5.3 Particles and quasiparticles
4. 5.4 Broken symmetry
5. Exercises
6. Solutions
3. 6 Superfluidity
1. 6.1 Non-interacting Bose gas
2. 6.2 Field theory for interacting Bose gas
3. 6.3 The condensate
4. 6.4 Excitations as oscillations
5. 6.5 Topological excitations
6. Exercises
7. Solutions
10. Part III Fields and Radiation
1. 7 Classical fields
1. 7.1 Chain of coupled oscillators
2. 7.2 Continuous elastic string
3. 7.3 Classical electromagnetic field
4. Exercises
5. Solutions
2. 8 Quantization of fields
1. 8.1 Quantization of the mechanical oscillator
2. 8.2 The elastic string: phonons
3. 8.3 Fluctuations of magnetization: magnons
4. 8.4 Quantization of the electromagnetic field
5. Exercises
6. Solutions
1. 9.1 Transition rates
2. 9.2 Emission and absorption: General considerations
3. 9.3 Interaction of matter and radiation
4. 9.4 Spontaneous emission by atoms
5. 9.5 Blue glow: Cherenkov radiation
6. 9.6 Bremsstrahlung
7. 9.7 Processes in lasers
8. Exercises
9. Solutions
4. 10 Coherent states
1. 10.1 Superpositions
2. 10.2 Excitation of an oscillator
3. 10.3 Properties of the coherent state
4. 10.4 Back to the laser
5. 10.5 Coherent states of matter
6. Exercises
7. Solutions
11. Part IV Dissipative Quantum Mechanics
1. 11 Dissipative quantummechanics
1. 11.1 Classical damped oscillator
2. 11.2 Quantum description
3. 11.3 Time-dependent fluctuations
4. 11.4 Heisenberg uncertainty relation
5. Exercises
6. Solutions
2. 12 Transitions and dissipation
1. 12.1 Complicating the damped oscillator: Towards a qubit
2. 12.2 Spin-boson model
3. 12.3 Shifted oscillators
4. 12.4 Shake-up and P(E)
5. 12.5 Orthogonality catastrophe
6. 12.6 Workout of P(E)
7. 12.7 Transition rates and delocalization
8. 12.8 Classification of environments
9. 12.9 Vacuum as an environment
10. Exercises
11. Solutions
12. Part V Relativistic Quantum Mechanics
1. 13 Relativistic quantummechanics
1. 13.1 Principles of the theory of relativity
2. 13.2 Dirac equation
3. 13.3 Quantum electrodynamics
4. 13.4 Renormalization
5. Exercises
6. Solutions
13. Index