Frontier Problems in Quantum Mechanics

Owing to efforts in both theoretical and experimental research, a better understanding of the interpretation and many fundamental principles of quantum mechanics has been achieved. These include the complementarity principle, the geometrical phase, the topological phase, the boundary between quantum and classical mechanics, quantum mechanics on the macroscopic level, and so on. Part of this book is devoted to introducing these developments.

Significant progress in the frontier research in various branches of physics has been achieved by making use of the insights and judgements originating from quantum mechanics. Part of this book is devoted to introducing some of these fields, namely quantum information, cavity quantum electrodynamics, the quantum Hall effect and the Bose–Einstein condensation. Basic physical ideas and methods are emphasized, instead of going into technical details.

The Yang–Baxter system has become a prosperous field of mathematical physics. The last part of the book is devoted to introducing its application to some basic problems in quantum mechanics, and again basic physical ideas are emphasized.

• Wave-Particle Dualism, Complementarity Principle, Bell's Theorem and Related Experiments
• Quantum Entanglement and Its Applications to Quantum Information and Quantum Computing
• Geometrical Phases in Quantum Mechanics
• Boundary between Quantum and Classical Mechanics, Entanglement and Decoherence
• Path Integral Formulation of Quantum Mechanics
• Quantum Mechanics on the Macroscopic Level
• Topological Phase Factors in Quantum Systems
• Cavity Quantum Electrodynamics, van der Waals Forces and Casimir Effect
• The Quantum Hall Effect
• Bose-Einstein Condensation
• The Yangian Commutation Relations in Quantum Mechanics
• RTT Relation and the Yang-Baxter Equation, Physical Significance of the Quantum Algebras