旋转磁场中的带电粒子
Charged particles in a rotating magnetic field
摘要：
本文研究了在旋转磁场中运动的碱金属原子或具有任意自旋和磁矩的一般带电粒子的价电子。利用含时么正变换，将哈密顿量含时的薛定谔方程化为有效哈密顿量与时间无关的类薛定谔方程.有效哈密顿量的本征态对应于原始薛定谔方程的循环解。无论该解是否明确可用，循环解的非绝热几何相都可以用沿着旋转轴的总角动量分量的期望值来表示。对于碱性原子电子和强磁场，完全解决了有效哈密顿量的本征值问题，几何相位是两个立体角的线性组合。对于弱磁场，同样的问题得到了部分解决。对于一般的带电粒子，在缓慢旋转的磁场中近似求解了该问题，并计算了几何相位。
英文摘要：
We study the valence electron of an alkaline atom or a general charged particle with arbitrary spin and with magnetic moment moving in a rotating magnetic field. By using a time-dependent unitary transformation, the Schrödinger equation with the time-dependent Hamiltonian can be reduced to a Schrödinger-like equation with a time-independent effective Hamiltonian. Eigenstates of the effective Hamiltonian correspond to cyclic solutions of the original Schrödinger equation. The nonadiabatic geometric phase of a cyclic solution can be expressed in terms of the expectation value of the component of the total angular momentum along the rotating axis, regardless of whether the solution is explicitly available. For the alkaline atomic electron and a strong magnetic field, the eigenvalue problem of the effective Hamiltonian is completely solved, and the geometric phase turns out to be a linear combination of two solid angles. For a weak magnetic field, the same problem is solved partly. For a general charged particle, the problem is solved approximately in a slowly rotating magnetic field, and the geometric phases are also calculated.
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