妙哉狄拉克函数  

The graceful Dirac function

作　　者：杨师杰 YANG Shi-jie(Department of Physics,Beijing Normal University,Zhuhai,Guangdong 519087,China)

机构地区：[1]北京师范大学文理学院物理学系,广东珠海519087

出　　处：《大学物理》2024年第10期10-12,29,共4页College Physics

摘　　要：本文从狄拉克δ函数出发,证明了球谐函数的加法公式,将数学物理中常用的积分变换统一为一般的Y-变换,并由此推导出一组原创的积分变换及其逆变换.我们还利用狄拉克函数重新对量子力学薛定谔方程进行演绎,避免了外势场中粒子平面波的假设,并由量纲分析自然地得到了德布罗意关系,为初学者理解量子力学提供了新的视角.Starting from Dirac's δ-function,we derive the sum rule of the spherical hamonics.We obtain a generalized y-transform which covers several traditional integral transformations.We also construct a new type of integral transformation and its inverse transformation.Furthermore,we introduce the Schrödinger's equation by making use of the Dirac function,which effectively avoid the plane wave hypothesis for a quantum particle moving in an external potential.The de Broglie matter wave relations are naturally derived via dimension analysis.Our method provides a new point of view to understanding quantum mechanics for students.

关 键 词：狄拉克δ函数 正交完备集 积分变换 y-变换 薛定谔方程 

分 类 号：O411[理学—理论物理]