量子力学教学中的几个数学细节
Some mathematic details of questions in teaching of quantum mechanics
任智1
作者信息
- 1. 百色学院 材料科学与工程学院,广西 百色 533000
- 折叠
摘要
量子力学波动力学分支是建立在算符、本征值方程和算符代数的数学形式之上的.通过对三个教学情境:(1)算符(xˆ),(pˆ)x不可易的推导过程;(2)位置算符的特征波函数的推导过程;(3)力学算符的运动方程推导过程,所涉及数学细节的理解和解释,展现了量子力学教学中数学概念的清晰、推导的逻辑严密性和对数学形式的多样性及其它们彼此之间转换的灵活性的熟练掌握对量子物理概念理解的重要性.
Abstract
Wave mechanics is one of branch of quantum mechanics using the mathematic formalism of operator,eigenvalue equation and operator algebra.Based on the analysis of the troubleshooting process of three mathematically related scenarios in quantum mechanical teaching,(1)commutation relation derivation of between operator (x ˆ)and (pˆ)x,(2)introduction of Eigen-function of position operator,(3)derivation of equation of motion of operator,the necessity of a mastery of clarity of mathematic definition,rigorousness in derivation and the knowledge of variety of mathematical forms and their mutual transformation among them,is shown to be vital for the real understanding of quantum mechanics.
关键词
算符/位置算符/运动方程/量子力学Key words
operator/position operator/equation of motion/quantum mechanics引用本文复制引用
出版年
2024
国家科技期刊平台
NSTL
万方数据