QUANTUM PHYSICS AND MODERN APPLICATIONS (PROB & SOL)

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.

Contents:

• Quantum Mechanics and Concepts:
  • Basic Quantum Concepts
  • Harmonic Oscillators
  • Dirac's Bra-Ket Formalism
• Spin Physics:
  • Introduction to Spin Physics
  • Spin Transformation
• Second Quantization and Applications:
  • Second Quantization
  • Dirac Delta Calculus
  • Condensed Matter Applications
• Non-equilibrium Green's Function:
  • Green's Function for Quantum Transport
  • Non-equilibrium Green's Function (NEGF)
• Gauge and Topology:
  • Coordinate Transformation
  • Berry-Pancharatnam Gauge
  • Non-Abelian Gauge
  • Topology and Gauge
• Advanced Condensed Matter Physics:
  • Crystal Lattice and Band Structure
  • Entanglement Entropy
• General Physics:
  • Minimization Physics
  • Electron Physics and Visualizations
  • Mathematical Methods
• Quantum Computation and Information:
  • Quantum States of Qubits
  • Quantum Gates and Circuits

Readership: Undergraduates, advanced undergraduates and postdocs in physics and materials science.

Key Features:

• Problems are designed across a broad spectrum of modern research topics, e.g. QCI, NEGF for nanoscale electronics and spintronics, gauge and topology in new materials
• Solutions are explicit and self-explanatory
• Solutions are substantiated with remarks and reflections, making them more accessible to self-learners