物理学中的“降维打击”

SOLVING PHYSICAL PROBLEMS IN HIGHER DIMENSIONAL SPACE

维度是物理学习和研究中的一个重要概念。在处理复杂物理问题时,通常采用降维的方法对问题进行简化,进而在低维空间中对简化后的问题进行分析和求解。然而在面对具体物理问题时,有时候增加系统的维度反而会使问题的分析变得更加直观和简单。本文以几个具体的物理问题为例,展示如何通过提升系统的维度来有效解决低维中遇到的一些困难。本文旨在强调“降维打击”思想在物理教学中的意义,目的在于培养学生的发散思维能力。

Dimension is an important concept in physics learning and research.In dealing with complicated physical problems,dimensionality reduction methods are often used to simplify the problem,so as to analyze and solve the simplified problem in a low dimensional space.However,when faced with specific physical problems,sometimes increasing the dimensions of the system can make the problem become more intuitive and simpler.This paper takes sev-eral specific physical problems as examples such as Gaussian integral,determinant calcula-tion,normalizing the eigenstates of the harmonic oscillator in quantum mechanics,and gener-ating functions of special functions,to demonstrate how to effectively solve the difficulties en-countered in low dimensional teaching by improving the dimensions of the system.The pur-pose of this paper is to emphasize the significance of the concept of“dimension reduced strate-gy”in physics teaching,and cultivate students􀆳divergent thinking abilities.