Bloch Electrons in a Uniform Magnetic Field
Bloch Electrons in a Uniform Magnetic Field
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均匀磁场中的布洛赫电子
DOI：
10.1103/physrev.133.a1038
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发表时间：
1964
期刊：
影响因子：
--
通讯作者：
E. Brown
中科院分区：
文献类型：
--
作者：
E. Brown
均匀磁场的存在不会破坏空间晶格的物理周期性。结果表明，在这种情况下，与纯平移同构的酉算符的射线群与哈密顿量交换。这种群具有如下特征性质：$AB=\mathm{exp}[I\ensureath{\varphi}(A，B)]C$，其中$A$、$B$和$C$是群的元素，$\ensureath{\varphi}$是数值因子。将表象理论应用于该群，得到了磁场中能级的特征简并，以及本征函数的变换性质。通过这些方法，可以构造出适用于晶体中有限磁场的有效哈密顿量。
The physical periodicity of a space lattice is not destroyed by the presence of a uniform magnetic field. It is shown that a ray group of unitary operators, isomorphic to pure translations, commutes with the Hamiltonian in this case. Such a group has the characteristic property that $AB=\mathrm{exp}[i\ensuremath{\varphi}(A,B)]C$, where $A$, $B$, and $C$ are elements of the group and $\ensuremath{\varphi}$ is a numerical factor. Representation theory applied to this group yields the characteristic degeneracies of levels in magnetic fields, as well as the transformation properties of eigenfunctions. By means of these it is possible to construct an effective Hamiltonian appropriate to finite magnetic fields in crystals.