1Chapter-1
141Qubit Representation:
2Review of Basic Quantum Mechanics
142Quantum Gates:: Practice Problem 1:
31.1 The Schrödinger Equation: Practice Problems:
14311.2 Quantum Algorithms and Quantum Circuits
41.2 Quantum States and Wavefunctions: Practice Problems:
144Quantum Parallelism and Quantum Fourier Transform:
51.3 Observables and Measurement: Practice Problems:
145Grover’s Search Algorithm:
61.4 Uncertainty Principle: Practice Problems:
146Shor’s Factoring Algorithm:
71.5 Postulates of Quantum Mechanics: Practice Problems:
147Quantum Error Correction:
81.6 Simple Quantum Systems
148Solved Example 2: Grover’s Search Algorithm: Practice Problem 2:
9Particle in a Box:
14911.3 Quantum Teleportation and Entanglement
10Harmonic Oscillator:
150Entanglement:
11Hydrogen Atom:
151Quantum Teleportation Protocol:: Practice Problem 3:
12Practice Problems:
15211.4 Quantum Error Correction and Decoherence
13Conclusion
153Decoherence and Quantum Errors:
14Chapter-2
154Quantum Error Correction:: Practice Problem 1:
15Linear Algebra in Quantum Mechanics
15511.5 Quantum Cryptography and Communication
162.1 Hilbert Space Formalism: Practice Problems:
156Quantum Key Distribution (QKD):
172.2 Operators and Eigenvalue Problems: Practice Problems:
157Quantum Communication Protocols:: Practice Problem 2:
182.3 Change of Basis and Unitary Transformations: Practice Problems:
15811.6 Quantum Simulation and Quantum Annealing
192.4 Tensor Products and Many-Particle Systems: Practice Problems:
159Quantum Simulation:
202.5 Hermitian and Unitary Operators
160Quantum Annealing:: Practice Problem 3:
21Hermitian Operators:
161Conclusion
22Unitary Operators:
162Chapter 12
23Practice Problems:
163Advanced Topics in Quantum Mechanics
242.6 Spectral Theorem and Projection Operators: Practice Problems:
16412.1 Density Functional Theory
25Conclusion
16512.2 Path Integral Formulation of Quantum Mechanics
26Chapter-3
16612.3 Quantum Field Theory and Second Quantization
27Time Evolution in Quantum Mechanics
167Solved Examples and Practice Problems
283.1 The Time-Dependent Schrödinger Equation
168Practice Problem 1:
29Example:: Practice Problem:
169Practice Problem 2:: Practice Problem 3:
303.2 Stationary States and Time-Independent Hamiltonians
17012.4 Topological Quantum Mechanics
31Example:: Practice Problem:
17112.5 Non-Equilibrium Quantum Mechanics
323.3 Time Evolution Operator and Propagator
17212.6 Relativistic Many-Body Theory
33Example:: Practice Problem:
173Solved Examples and Practice Problems
343.4 Quantum Mechanical Expectation Values
174Practice Problem 1:
35Example:: Practice Problem:
175Practice Problem 2:: Practice Problem 3:
363.5 Ehrenfest’s Theorem and Classical Limit
176Conclusion
37Example:: Practice Problem:
177Chapter 13
383.6 Quantum Dynamics in the Heisenberg Picture
178Quantum Optics and Atomic Physics
39Example:: Practice Problem:
17913.1 Quantization of the Electromagnetic Field
40Conclusion
18013.2 Interaction of Atoms with Electromagnetic Radiation
41Chapter 4
18113.3 Laser Theory and Coherent States
42Symmetries in Quantum Mechanics
182Solved Examples and Practice Problems
434.1 Rotational Invariance and Angular Momentum
183Practice Problem 1:
444.2 Orbital Angular Momentum and Spin
184Practice Problem 2:: Practice Problem 3:
45Orbital Angular Momentum:: Spin Angular Momentum:
18513.4 Cavity Quantum Electrodynamics
464.3 Addition of Angular Momenta
18613.5 Atom Cooling and Trapping Techniques
474.4 Parity and Time-Reversal Symmetry
1871. Laser Cooling :
48Parity Symmetry:
1882. Evaporative Cooling :
49Time-Reversal Symmetry:
1893. Magnetic Trapping :
50Combined Parity and Time-Reversal Symmetry:
1904. Optical Trapping :: 5. Hybrid Trapping Techniques :
514.5 Continuous Symmetries and Noether’s Theorem: Noether’s Theorem:
19113.6 Quantum Measurement and Weak Measurements
524.6 Discrete Symmetries and their Implications
192Solved Examples and Practice Problems
53Charge Conjugation (C) Symmetry:
193Practice Problem 1:
54CP Symmetry:
194Practice Problem 2:: Practice Problem 3:
55Implications of CP Violation:
195Conclusion
56Conclusion
196Chapter 14
57Chapter 5
197Condensed Matter Applications
58Approximation Methods in Quantum Mechanics
19814.1 Electron Gas and Band Theory of Solids
595.1 Time-Independent Perturbation Theory: Non-Degenerate Perturbation Theory:
19914.2 Superconductivity and the BCS Theory
605.2 Variational Principle and Variational Method
20014.3 Fractional Quantum Hall Effect
61Variational Principle:: Variational Method:
201Solved Examples and Practice Problems
625.3 Degenerate Perturbation Theory
202Practice Problem 1
635.4 Wentzel-Kramers-Brillouin (WKB) Approximation
203Practice Problem 2
645.5 Adiabatic Theorem and Berry Phase: Berry Phase:
204Practice Problem 3
655.6 Born-Oppenheimer Approximation
205Practice Problem 4
66Conclusion
206Practice Problem 5
67Chapter 6
20714.4 Quantum Phase Transitions and Strongly Correlated Systems
68Scattering Theory
20814.5 Quantum Transport and Mesoscopic Physics
696.1 Scattering Cross-Section and Differential Cross-Section
20914.6 Topological Insulators and Topological Order
706.2 Partial Wave Analysis and Phase Shifts
210Solved Examples and Practice Problems
716.3 Optical Theorem and Optical Potentials: Optical Potentials:
211Practice Problem 1
726.4 Lippmann-Schwinger Equation and T-Matrix: The T-Matrix:
212Practice Problem 2
736.5 Quantum Mechanical Tunneling
213Practice Problem 3
746.6 Resonance Scattering and Feshbach Resonances: Feshbach Resonances:
214Practice Problem 4
75Conclusion
215Practice Problem 5
76Chapter 7
216Conclusion
77Relativistic Quantum Mechanics
217Chapter 15
787.1 Klein-Gordon Equation
218Nuclear and Particle Physics Applications
797.2 Dirac Equation and Spin-1/2 Particles
21915.1 Quantum Mechanical Description of the Nucleus
807.3 Lorentz Covariance and Dirac Matrices
220Nucleon Motion and the Nuclear Potential
81Solved Examples:
221Nuclear Shell Model
82Practice Problems:
222Nuclear Spin and Magnetic Moment
83Solutions to the practice problems:
223Nuclear Stability and Radioactivity
847.4 Hydrogen Atom in Relativistic Quantum Mechanics
22415.2 Nuclear Models and Nuclear Reactions
857.5 Negative Energy Solutions and Antiparticles
225Liquid Drop Model
867.6 Quantum Electrodynamics (QED) and Feynman Diagrams
226Shell Model
87Solved Examples:
227Nuclear Reactions
88Practice Problems:
22815.3 Fundamental Interactions and Particle Physics
89Solutions to the practice problems:
229Fundamental Interactions
90Conclusion
2301. Strong Nuclear Force
91Chapter 8
2312. Electromagnetic Force
92Quantum Theory of Radiation
2323. Weak Nuclear Force: 4. Gravitational Force
938.1 Second Quantization and Fock Space
233Elementary Particles
948.2 Quantization of the Electromagnetic Field
234Leptons:
958.3 Interaction of Radiation with Matter
235Quarks:
96Solved Examples:: Practice Problems:
236Particle Accelerators and Detectors
978.4 Spontaneous and Stimulated Emission
23715.4 Gauge Theories and the Standard Model
98Spontaneous Emission:: Stimulated Emission:
238Gauge Invariance and Local Gauge Theories
998.5 Density Matrices and Open Quantum Systems
239The Standard Model of Particle Physics
100Density Matrices:: Open Quantum Systems:
240Electroweak Unification
1018.6 Dissipation and Decoherence
24115.5 Quantum Chromodynamics and Confinement
102Dissipation:
242Color Charge and Gluons
103Decoherence:
243Confinement and Hadronization
104Solved Examples:
244Asymptotic Freedom
105Practice Problems:
245QCD Phenomenology and Applications
106Solutions to the practice problems:
246Asymptotic Freedom Explained:
107Conclusion
24715.6 Neutrino Physics and Neutrino Oscillations
108Chapter 9
248Neutrino Masses and Flavor Mixing
109Many-Body Quantum Mechanics
249Neutrino Oscillation Experiments
1109.1 Identical Particles and Symmetrization
250Neutrino Masses and Beyond the Standard Model
1119.2 Bosons, Fermions, and the Pauli Exclusion Principle
251Conclusion
1129.3 Second Quantization for Many-Body Systems
252Chapter 16
113Solved Examples:: Practice Problems:
253Quantum Gravity and Cosmology
1149.4 Occupation Number Representation
25416.1 Canonical Quantization of General Relativity
1159.5 Electron Gas and Fermi Liquid Theory
255General Relativity and the Need for Quantum Gravity
116Electron Gas:: Fermi Liquid Theory:
256Canonical Quantization Approach
1179.6 Bose-Einstein Condensation
257Wheeler-DeWitt Equation
118Conclusion
258Challenges and Limitations
119Chapter 10
25916.2 String Theory and M-Theory
120Time-Dependent Perturbation Theory
260String Theory: A Unified Framework
12110.1 Transition Probabilities and Fermi’s Golden Rule
261Strings and Vibrational Modes
122Transition Probabilities:
262Superstrings and Supersymmetry
123Fermi’s Golden Rule:: Practice Problem 1:
263M-Theory and Branes
12410.2 Interaction Picture and Dyson Series
264String Theory Implications and Challenges
125Interaction Picture:
265String Theory Implications and Challenges
126Dyson Series:: Practice Problem 2:
26616.3 Loop Quantum Gravity and Spin Networks
12710.3 Sudden and Adiabatic Approximations
267Canonical Quantization and the Loop Representation
128Sudden Approximation:: Practice Problem 3:
268Spin Networks and Quantum Geometry
129Adiabatic Approximation:: Practice Problem 4:
269Discreteness and Quantum Fluctuations of Spacetime
130Rabi Oscillations:: Practice Problem 1:
270Black Hole Entropy and the Bekenstein-Hawking Formula
131Rotating Wave Approximation (RWA):: Practice Problem 2:
271Challenges and Future Prospects
13210.5 Time-Dependent Variational Principle: Practice Problem 3:
27216.4 Quantum Effects in the Early Universe
13310.6 Applications in Atomic, Molecular, and Solid-State Physics
27316.5 Black Holes, Hawking Radiation, and Thermodynamics
134Atomic Physics:
27416.6 Quantum Cosmology and the Multiverse
135Molecular Physics:
275Solved Examples:
136Solid-State Physics:: Practice Problem 4:
276Practice Problems:
137Conclusion
277Conclusion
138Chapter 11
278Glossary
139Quantum Computing and Information
279Index
14011.1 Qubits and Quantum Gates
