一维无限深梯形势阱中微观粒子波函数和能级的半解析解  

The semi-analytical solution of wave functions and energy levels of a micro-particle in one-dimensional infinite trapezoid potential well

作　　者：罗强[1] 姜玉梅[1] 韩玖荣[1] 苏垣昌[1] 

机构地区：[1]扬州大学物理科学与技术学院,江苏扬州225002

出　　处：《大学物理》2014年第6期55-60,共6页College Physics

摘　　要：利用特殊函数研究了一个数学形式简单但物理内涵丰富的新势阱——一维无限深梯形势阱,并得到了处于该势阱中微观粒子的波函数和能级的半解析解,其结果可以用来从理论上分析梯形沟道势阱的二维电子气的物理机制.此外指明了它与熟知的一维无限深方势阱和三角势阱的联系与区别,并基于对应原理讨论了该模型下粒子波函数的特征.A new type of potential well, namely one dimensional infinitely trapezoid potential well, which is simple in form but rich in content, is studied by us with the help of special functions and the semi-analytical solutions of the wave functions and energy levels for a micro-particle confined into it is obtained. Those results can help us better understand the physical mechanism of the two-dimensional electron gas in trapezoid channel potential well. Besides, the connection and difference between the model proposed in this paper and the well-known models, i.e. rectangular/triangular potential well are illustrated. We also discuss the properties of the wave function based on the correspondence principle.

关 键 词：梯形势阱 波函数 能级 对应原理 

分 类 号：O413.1[理学—理论物理]