正弦平方势与带电粒子沟道效应的能带结构

在量子力学的框架内描述了带电粒子与晶体相互作用，利用正弦平方势把沟道粒子的Schr?dinger方程化为Mathieu方程，根据Bloch定理讨论了系统能量分布，并用摄动法求解了方程的低阶不稳定区及其禁带宽度，系统自动呈现出了能带结构，再现了粒子束同晶体相互作用的周期性特征.而这一点正是其他相互作用势不曾有的. 关键词： 沟道效应 能带结构 正弦平方势 摄动法

The sine-squared potential and the band structure for channelling effects

The interaction between the charged particle and the crystal is described by quantum mechanics. The schrdinger equation describing a paticle moving in the channel is reduced to Mathieu equation by using a sine-squared potential. The band structure of this system is discussed based on Bloch theorem. The instability zone and the stop-band width are found by the perturbation techniques. It is shown that the width of the 1-st order and 2-nd order instability zones are ΔE₁=Kβ/2 and ΔE₂=md²_p(Kβ)²/16π²², respectively, and this system presents automatical the band structure, which is not present in Lindhard potential and Moliere potentials.