小尺寸金属纳米粒子光学性质的理论研究

Theoretical Research of Optical Property of Small Sizes Metallic Nanoparticles

半经典理论不能解析求解传导电子平均场近似势的Schrlinger方程,为了克服这种不足,用一种多台阶势近似的方法处理Woods-Saxon型势,准确地得到了能级和分段解析波函数,从而将半经典量子理论模型推广为完全的量子理论模型,并用这个模型计算了小尺寸金属纳米粒子(钠原子)表面等离子体的共振频率,结果与采用局域密度近似(LDA)方法计算的一致。

Semiclassical theory couldn＇t be used to analyze and solve the Schroedinger equation of conduction electron＇s average field approximate potential. In order to overcome the insufficiency, an approach of a multi-step potential approximation was adopted to deal with the Woods-Saxon potential. And its accurate energy and subsection analytical wave function were then obtained. Thus, the model of semiclassical theory could be extended to a complete quantum theory model. The surface plasmon＇s resonance frequency of small sizes metallic nanoparticles （sodium atom） was calculated by using this model. The result is in quantitative agreement with that achieved by local density approximation （LDA）