自旋1／2和自旋1系统在一维变化磁场中的精确解和Aharonov－Anandan相

THE EXACT SOLUTION AND AHARONOV-ANANDAN PHASE FOR SPIN 1/2 AND SPIN 1 SYSTEMS IN ONE DIMENSIONAL VARIED MAGNETIC FIELDS

本文首先根据Ｍｉｚｒａｈｉ构造不变量的方法建立了在一维变化磁场中自旋ｊ系统的不变量，然后利用自旋１／２和自旋１系统不变量的简明矩阵形式直接求解不变量的本征波函数，由此给出了该系统含时Ｓｃｈｒｏｄｉｎｇｅｒ方程的精确解，进而根据Ｌｅｗｉｓ相讨论了此系统的Ａｈａｒｏｎｏｖ－Ａｎａｎｄａｎ相。

In this paper, we construct invariants of spin-j system in one dimensional varied magnetic fields in terms of Mizrahi's method for constructing invariants, then we apply simple matrix of spin and spin-j invariants to solve eigenfunctions of invariants. From this we get the exact solution of the time-dependent Schrodinger equation for this system. According to Lewis phase, we discuss Aharonov-Anandon phase.