Panati Gianluca, Spohn Herbert, Teufel Stefan
Zentrum Mathematik and Physik Department, TU München, D-80290 München, Germany.
Phys Rev Lett. 2002 Jun 24;88(25 Pt 1):250405. doi: 10.1103/PhysRevLett.88.250405. Epub 2002 Jun 11.
A systematic perturbation scheme is developed for approximate solutions to the time-dependent Schrödinger equation with a space-adiabatic Hamiltonian. For a particular isolated energy band, the basic approach is to separate kinematics from dynamics. The kinematics is defined through a subspace of the full Hilbert space for which transitions to other band subspaces are suppressed to all orders, and the dynamics operates in that subspace in terms of an effective intraband Hamiltonian. As novel applications, we discuss the Born-Oppenheimer theory to second order and derive for the first time the nonperturbative definition of the g factor of the electron within nonrelativistic quantum electrodynamics.
针对具有空间绝热哈密顿量的含时薛定谔方程，开发了一种系统微扰方案以获得近似解。对于特定的孤立能带，基本方法是将运动学与动力学分离。运动学通过全希尔伯特空间的一个子空间来定义，在该子空间中，到其他能带子空间的跃迁被抑制到所有阶次，而动力学则在该子空间内依据有效的带内哈密顿量进行操作。作为新颖的应用，我们讨论了二阶的玻恩 - 奥本海默理论，并首次在非相对论量子电动力学中推导出电子g因子的非微扰定义。
