建立了有限对一维铁磁性和非磁性层交错组成的周期系统，应用布洛赫自旋波量子理论，研究了该系统的基本性质及电子波函数散射特征对交错层数量依赖的关系。研究发现：在系统中电子波函数可表示为无限周期系统中转换矩阵特征向量的叠加或类布洛赫函数，解此函数可得到任意层数系统的单色波散射的精确解。在此基础上，导出了电子波函数在周期系统中反射系数和透射系数对能量的依赖关系。对光谱窗口的计算发现其势能和宽度几乎与全反射区域一样。该系统由于高能量的传输和在电子自旋方向上对交换能的依赖而可能用于自旋滤波器。%We establish a general model of a finite periodic system by n pairs of alternating ferromagnetic and nonmagnetic (FNF) layers. Using Bloch spin wave quantum theory, the basic properties of alternating FNF layers and the dependence of property of electron wave scattering in alternating layers on the number of layers are investigated. It is found that an electron wavefunction in the system can be expressed as the superposition of eigenvectors of a transfer matrix or Bloch-like functions in an infinite periodic system. Form this function we can obtain an exact solution for monochromatic wave scattering of a system with an arbitrary number of layers. On this basis, the dependences of reflection and transmission coefficients on energy for the electron wavefunction in a periodic system are determined. The calculation of spectral window shows that its energy position and width are the same as those of almost full reflection region. The system can be used as spin filter due to high-energy dispersion and dependence of exchange energy on electron spin direction.
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