內容簡介
《量子系統中的幾何相位》Aimed at graduate physics and chemistry students, this is the first comprechenslve monograph covering the concept of the geometric phase in quantum physics from its mathematical foundations to its physical applications and experimental manifestations. It contains all the premises of the adiabatic Berry phase as well as the exact Anandan-Aharonov phase. It discusses quantum systems in a classical time-independent environment (time dependent Hamiltonians) and quantum systems in a changing environment (gauge theoryofmolecular physics). The mathematical methods used are a combination of differential geometry and the theory of Iinear operators in Hilbert Space. As a result, the monograph demonstrates how non-trivial gauge theories naturally arise and how the consequences can beexperimentallyobserved. Readers benefit by gaining a deep understanding of the long-ignored gauge theoretic effects of quantum methanics and how to measure them.
目錄
1 Introduction
2 Quantal Phase Factors for Adiabatic Changes
2.1 Introduction
2.2 Adiabatic Approximation
2.3 Berry's Adiabatic Phase
2.4 Topological Phases and the Aharonov-Bohm Effect Problems
3 Spinning Quantum System in an External Magnetic Field
3.1 Introduction
3.2 The Parameterization of thebasisVectors
3.3 Mead-Berry Connection and Berry Phase for Adiabatic Evolutions - Magnetic Monopole Potentials
3.4 The Exact Solution of the SchrSdinger Equation
3.5 Dynamical and Geometrical Phase Factors for Non-Adiabatic Evolution Problems
4 Quantal Phases for General Cyclic Evolution
