浅析自由粒子的薛定谔方程的解  

Analysis of the Solution of Schrdinger Equation for Free Particle

作　　者：罗光[1] 

机构地区：[1]重庆师范大学物理与电子工程学院,重庆401331

出　　处：《重庆师范大学学报（自然科学版）》2014年第2期77-79,共3页Journal of Chongqing Normal University:Natural Science

基　　金：重庆市科委自然科学基金(No.cstc2012jjA50018);重庆市教委理科科研项目(No.KJ120613)

摘　　要：基于自由粒子满足的薛定谔方程,文章对此方程作了深入讨论,得出方程仅有平庸解。另外,从一维无限深势阱在势阱宽度为无限宽和一维方势垒在势垒高度趋于零这两种极限情况下,同样得到平庸解。虽然是平庸解,却说明了某些和经典力学一致的内容,说明了经典力学和量子力学之间的联系。该平庸解说明:1)对于无限自由粒子,遵循牛顿第一运动定律的规律;2)对于无限自由粒子,不表现物质波波动的特性,只有在有约束(或者相互作用)的情况下,才体现波粒二象性的统一。Based on the theory of Schr6dinger equation for the free particle, the solution of that equation was discussed in detail. It is found that the equation only exist an insignificant solution. And the mediocre solution can be also obtained from the one-dimensional infinitely deep potential well in a potential well width tending to infinite and from one-dimensional square potential barrier in the bar- rier height tending to zero. Although the solution is insignificant, but it describes some ideal that is consistent with that of classical mechanics. It explains the connection between the classical mechanics and quantum mechanics. The mediocre solutions show that 1） For infinite free particles, it is followed by Newton＇ s first motion law, 2） For infinite free particle, it does not exist matter wave characteristics. Only if there is some potential （i. e. interactions）, the Wave-particle duality be embodied.

关 键 词：薛定谔方程 自由粒子 量子力学 经典力学 

分 类 号：O413.1[理学—理论物理]