Preface
Although quantum theory has been older than hundred years, its capacity to produce counterintuitive insights into the nature remains undiminished. The phenomenon of entanglement noted by Erwin Schrödinger earlier in 1935 has become a valuable source in quantum information processing which is still a remarkably young research field. Since Yakir Aharonov and David Bohm predicted the so-called AB effect in 1959, more and more roles that phase plays in quantum theory were revealed. Along with the rapid developments in nanotechnology, people have been attempting to utilize quantum states to build a quantum computer. As a follow-up course of Lectures on Quantum Mechanics, the present course provides an introduction to some of the modern developments in the aforementioned aspects.
Starting from the earlier attempts to establish relativistic theories in Chapter 1, we introduce the Dirac equation and illustrate the physics im-plied in this equation. We hope the students perceive the fact that the emergence of electron spin is a relativistic effect, and meanwhile, get to know some current modern topics in frontiers of physics, such as Rashba spin-orbit coupling in certain semiconductors and the realization of mass-less Dirac fermions in graphene. In Chapter 2, we introduce the density matrix that is an important concept to describe quantum coherence. In Chapter 3, we introduce the concept of quantum entanglement and give a brief description of the Bennett's quantum teleportation proposal. We also introduce some primer concepts for quantum computation. In Chapter 4, we discuss the role of phases in quantum mechanics: Aharonov-Bohm ef-fect represents the topological phase, Berry phase is a geometric phase, and the formation of band structure is due to the dynamical phase. Finally, in Chapter 5 we revisit several approximation methods that are frequently applied in various research fields.
Acknowledgements
The authors would like to acknowledge Lingyun Deng and Yehua Liu for plotting the figures in the textbook. Careful reading of the manuscript by Ningju Hui, Yehua Liu, and Shan Zhu is also very much appreciated.
Youquan Li and Lihua Lü
Hangzhou,2016