Introduction to average Hamiltonian theory. I. Basics
Introduction to average Hamiltonian theory. I. Basics
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DOI：
10.1002/cmr.a.21414
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发表时间：
2016-11-01
影响因子：
0.6
通讯作者：
Brinkmann, Andreas
中科院分区：
文献类型：
--
作者：
Brinkmann, Andreas
在磁共振实验中理解电子或核自旋的动力学需要求解自旋系统的薛定谔方程，考虑自旋相互作用及其周围环境对哈密顿量的所有贡献。一般来说，这是一项困难的任务，因为这些相互作用项可以是时间依赖的，并且可能彼此不互换。平均哈密顿量理论是一种分析近似时间演化的有力工具，它用与时间无关的有效哈密顿量代替了含时哈密顿量。有效哈密顿量服从马格努斯展开，允许计算有效哈密顿量到一定的阶数。本文的目的是介绍平均哈密顿理论的严格，但教育的方式。在NMR光谱中的两个复合脉冲的应用是用来证明平均哈密顿理论的重要方面。
Understanding the dynamics of electron or nuclear spins during a magnetic resonance experiment requires to solve the Schrodinger equation for the spin system considering all contributions to the Hamiltonian from interactions of the spins with each other and their surroundings. In general, this is a difficult task as these interaction terms can be both time-dependent and might not commute with each other. A powerful tool to analytically approximate the time evolution is average Hamiltonian theory, in which a time-independent effective Hamiltonian is taking the place of the time-dependent Hamiltonian. The effective Hamiltonian is subjected to the Magnus expansion, allowing to calculate the effective Hamiltonian to a certain order. The goal of this paper is to introduce average Hamiltonian theory in a rigorous but educational manner. The application to two composite pulses in NMR spectroscopy is used to demonstrate important aspects of average Hamiltonian theory.