Bloch oscillations in one-dimensional solids and solitary wave packets
Bloch oscillations in one-dimensional solids and solitary wave packets
复制标题
一维固体和孤立波包中的布洛赫振荡
DOI：
10.1063/1.526825
复制
发表时间：
1985
影响因子：
1.3
通讯作者：
M. Luban
中科院分区：
文献类型：
--
作者：
M. Luban
我们导出了在恒定均匀电场存在下理想化的一维周期固体中电子的单带含时薛定谔方程的精确解。我们证明了所有的波函数在时间上必然是周期性的。这个结果是由准经典动力学预测的著名布洛赫振荡的完全量子力学模拟。我们的求解方法包括将电子薛定谔方程映射到在程函极限下的量子平面转子的精确可解问题，该问题受到任意角度和时间相关的外部势的影响。电子波函数的时间周期性是由于所有转子波函数都具有孤立波包的形式。
We derive the exact solution of a single‐band time‐dependent Schrodinger equation for an electron in an idealized one‐dimensional periodic solid in the presence of a constant uniform electric field. We show that all wave functions are necessarily periodic in time. This result is the fully quantum‐mechanical analog of the well‐known Bloch oscillations predicted by quasiclassical dynamics. Our method of solution consists of mapping the electron Schrodinger equation to the exactly solvable problem of a quantum planar rotor in the eikonal limit subject to an arbitrary angular and time‐dependent external potential. The time periodicity of the electron wave functions is due to the fact that all of the rotor wave functions have the form of solitary wave packets.