三角形在位势下一维无限深势阱中粒子的量子特性研究  

Research on Quantum Properties of Particle Trapped in One-Dimensional Infinite Potential Well with Triangular On-Site Potential

作　　者：向少华[1] 赖青青[1] 陈英[1] 

机构地区：[1]怀化学院电气与信息工程学院,湖南怀化418008

出　　处：《怀化学院学报》2015年第11期35-38,共4页Journal of Huaihua University

基　　金：湖南省教育厅教改项目"基于创新素质培养为目标的物理学专业课程体系的构建与实践研究"(湘教通[2012]401号);怀化学院教改课题"基于创新素质培养为目标的物理学专业课程体系的构建与实践研究"(201202)

摘　　要：利用有限差分方法数值求解了具有三角形在位势的一维无限深势阱中粒子的运动学方程,讨论了在位势对粒子几个最低能量本征值和与其对应的概率密度分布函数的影响.结果表明:粒子的最低能量随在位势强度的增加而增大,而它们的概率密度分布函数则呈现各不相同的空间特性.基态概率密度分布函数的波峰朝左移动,第一激发态的波峰朝右移动,而第二激发态的两侧波峰被削弱,中心峰被增强.The equation of motion for wave function of a particle trapped in one - dimensional infinite potential well with atriangular on - site potential is solved numerically by means of the finite difference method. The effect of the on - site potential onthe first few energy levels and the corresponding probability densities is discussed. It is shown that the minimum energies of theparticle increase with the increasing of the on - site potential, whereas their probabilities are completely different from each other inthe spatial distribution. When increasing the on - site potential, the wave crest of the ground state probability density can move tothe left and that of the first excited state will move to the opposite direction. For the second excited state, the increase of thecentral wave - crest amplitude is observed and on the contrary, the wave crests in both sides are suppressed.

关 键 词：量子力学 无限深势阱 三角形在位势 有限差分法 

分 类 号：O413.1[理学—理论物理]