480 pages, 10x7 inches
April 2003  Hardcover
ISBN 1-58949-010-X
US$78

 
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This book is based on lecture notes developed in last twenty two years during which the authors have been teaching a core graduate course, Quantum Mechanics II, at Fudan University. It covers a very broad range of topics, presenting the state of the art in Quantum Mechanics. Discussions on some topics such as Levinson theorem, Casimir effect, the essence of special relativity, the interpretation of wave function, geometric phase, fractional statistics, and paradoxes in quantum mechanics, reflect to some extent the authors' own research results. The book is profound, practical, enlightening, and pleasantly readable. It is not only a very good textbook for students majoring in theoretical, experimental, or applied physics, but also a very useful reference for researchers as well. 


graduate students, teachers, researchers in (both theoretical and experimental) quantum physics.
 

PREFACE.

CH.1.  Basic Concepts and Methods in Quantum Mechanics.
1.1. Spin system.
1.2. State vector, operator, matrix representation.
1.3. Configuration space representation, Wave function, Schrodinger equation.
1.4. Simple harmonic oscillator.
1.5. Uncertainty relation in measurement.
1.6. Coherent state, squeezed state.
1.7. Path integral, Green function.
App.1a. Some theorems in operator algebra.

CH.2.  Theory of Quantum Scattering.
2.1. Rigorous solution for elastic scattering.
2.2. Born approximation.
2.3. Partial wave method.
2.4. Levinson theorem.
2.5. Scattering of low energy neutron with proton, nuclear force.
2.6. Evolution operator and S matrix.
2.7. Transition probability, cross section.
2.8. Scattering and collision in two potentials.
2.9. Black nucleus model.

CH.3. Symmetries and Angular Momentum in Quantum Mechanics.
3.1. Introduction.
3.2. Rotated state and rotated operator.
3.3. General properties of angular momentum operator.
3.4. Coupling of two angular momenta, Clebesh-Gordan coefficient.
3.5. Matrix representation of rotation operator, D function
3.6. Irreducible tensor operator, Wigner-Eckart theorem and selection rules.
3.7. Symmetry and conservation law.
3.8. Space inversion, parity.
3.9. Time reversal symmetry.

CH.4.  Quantization of Electromagnetic Field and its Interaction with Charged Particles.
4.1. Coulomb gauge of electromagnetic field, total Hamiltonian of charged particle and electromagnetic field.
4.2. Plane wave solution of free electromagnetic field and its quantization.
4.3. Spherical wave solution of free electromagnetic field and its quantization.
4.4. Transition probability of electromagnetic multipole radiation. 		4.5. Estimation of magnitude for electromagnetic transition probability, selection rule. 
4.6. Casimir effect.

CH.5. Density Matrix and Quantum Statistics.
5.1. Density operator, ensemble.
5.2. Equation of motion for density matrix.
5.3. Polarization and scattering.
5.4. Introduction to quantum statistics.

CH.6. Phase in Quantum Mechanics.
6.1. Electromagnetic potential, gauge transformation.
6.2. Aharonov-Bohm effect, quantization of magnetic flux.
6.3. Adiabatic approximation, Berry phase.
6.4. Geometric phase in two-state system.

CH.7. Motion of Electron in Magnetic Fields.
7.1. Landau energy-level and degeneracy.
7.2. Introduction to quantum Hall effect.
7.3. Introduction to fractional statistics
7.4. Theory of composite boson, composite fermion.
7.5. Experimental discovery of fractional charge in FQHE.

CH.8. Methods in Quantum Many Body Problems and Applications.
8.1. Method of second quantization.
8.2. Hamiltonian in second quantization.
8.3. Bose-Einstein condensation.
8.4. Theory of superfluidity for liquid helium. 
8.5. BCS Theory for Superconductivity.

CH.9. Relativistic Quantum Mechanics.
9.1. Relativistic wave equation.
9.2. K-G equation and coupling to electromagnetic field.
9.3. Electron in electromagnetic field.
9.4. Klein paradox and anti-particle.
9.5. On the essense of special relativity.
9.6. Energy levels near the ground state of Hydrogen atom.
App.9a. A semi-quantiative calculation of the Lamb shift.

CH.10. Experiments and Interpretation of Quantum Mechanics.
10.1. Wave-particle duality, complementary principle, uncertainty relation.
10.2. Einstein-Podolsky-Rosen paradox and its test in experiments.
10.3. Quantum theory and physical reality.
App.10a. Quantum teloportation.
App.10b. Experimental study on Schrodinger's cat and its decoherence.

App. Convention units


 
Guang-jiong Ni is a Chair Professor of Physics in Fudan University, Shanghai. He has been teaching in Fudan for over 45 years and served as the director of Modern Physics Institute and the head of the Division for Theoretical Physics for many years. His research areas include quantum mechanics, field theory, and particle physics. He is the author for over 170 papers published in well known journals. Prof. Ni is a popular writer of science in China. His books Modern Physics (1979), Methods of Mathematical Physics (1989), Levinson Theorem, Anomaly and Phase Transition of Vacuum (1995), Physics Changing the World (1998), and Advanced Quantum Mechanics (2000) receive very warm welcome from very broad range of readers. He has received numerous rewards for his research, teaching activities and book writing. 

Su-qing Chen is a Professor of Physics in Fudan University, Shanghai. Before joining the Fudan faculty, she worked as a researcher in Shanghai Institute for Nuclei, mainly in the areas of nuclear theory, until 1978. In Fudan, Prof. Chen taught the courses Quantum Mechanics and Group Theory for many years. Her research work has been in theoretical physics, with  more than 20 publications. She is the co-author for two books "Levinson Theorem , Anomaly and Phase Transition of Vacuum " and "Advanced Quantum Mechanics". The former had been awarded the Science and Technology  Progress Prize by Education Ministry of China in 1999.
Su-qing married Guang-jiong in 1960, and they have been living a very happy life together since then.