Quantum Physics and Modern Applications: Problems and Solutions

This book is written with the view of providing learners a fast track into the modern applications of quantum physics. It is designed as a book of Problems and Solutions, consisting of more than 200 exercises with explicitly worked out solutions.

Focusing on modern research topics, the problems are designed to suit recent developments such as graphene, topological materials, spintronics, and quantum computation and information (QCI). Categorized into eight chapters, the book first introduces QM for undergraduates with an emphasis on the Dirac formalism and its representation in the form of matrices and functions. Chapter 2 is dedicated to spin physics, where the spinor formalism is increasingly relevant to research on spintronics, graphene, topological systems, Dirac, Weyl, and all branches of quantum information sciences. Chapter 3 deals with second quantization and its applications in nanoscience and condensed matter physics. Building on the foundations of the previous two chapters, Chapter 4 expounds on the non-equilibrium Green's Function (NEGF) - a modern topic with problems designed to suit applications in nanoscale electronic and spintronics systems. Chapter 5 covers gauge fields and topology, with a modern emphasis on applications in new materials such as graphene and topological systems. Chapter 6 comprises numerous advanced sub-topics in condensed matter physics as well as conventional topics such as band structures and entanglement entropy. Chapter 7 extends to cross-disciplinary and miscellaneous physics, where the topics are not necessarily quantum by nature, but deal with issues that have inspired the development of quantum mechanics and quantum fields. Lastly, the book caters to quantum computation with a preamble on the QM foundations of spin, projection, measurement and density matrices which underpin applications in quantum gates, quantum teleportation and entanglement.

Readers can expect a handy and effective guide in mastering problem solving techniques in frontier applications of quantum physics.

Seng Ghee Tan is a Professor in Physics at the Chinese Culture University, Taiwan. He obtained his PhD in quantum electronics and spintronics at the National University of Singapore (NUS). He was a Senior Research Fellow at the Agency for Science, Technology and Research (A*STAR, Singapore) from 2006 to 2009, before serving as Assistant Professor at NUS from 2009 to 2016. Prof. Tan was also a Visiting Professor at the National Taiwan University. His research interest broadly extends over quantum nanoscience and condensed matter systems, with milestone publications on spin-orbit interactions, spin-hall effects, graphene systems, topological insulators, and application of Yang-Mills physics in spintronics.

Ching Hua Lee is an Assistant Professor at the National University of Singapore (NUS). He obtained his BSc and PhD in theoretical condensed matter physics at Stanford University. His research interests include topological metamaterials/circuits, non-Hermitian physics, quantum circuit simulations, Floquet dynamics, nodal metals, strongly correlated electrons, quantum information and complex networks.

Mansoor B A Jalil is an Associate Professor in Electrical and Computer Engineering (ECE) Department at the National University of Singapore (NUS). He obtained his PhD at the University of Cambridge, UK. He was an adjunct staff at the Data Storage Institute, A*STAR, Singapore, an Assistant Professor at ECE Department, NUS, and served as Deputy Director of the NUS Nanoscience and Nanotechnology Initiative (NUSNNI). His research activities are focused on the theory and simulation of spintronic devices, topological materials like Weyl semimetals and two-dimensional conductors like graphene and silicene. Prof. Mansoor Jalil has published more than 250 papers in international peer-reviewed journals, given talks as a keynote speaker in the US, Japan, China, Israel and Korea, and contributed review articles and book chapters on spintronics and quantum devices.