德布罗意物质波关系式的推导

Derivation ofthe De Broglie matter wave equation

本文通过2种直观的方式推导出物质波动量-波长关系式.第1种方式利用洛伦兹变换得出运动粒子“首尾”两端固有时间差,进而通过其对应的相位差以及粒子在空间占据的长度得出相应的物质波波长;第2种方式通过计算与粒子相位变化相适配的行波,得出物质波动量-波长关系式.这两种推导方式较为直观,有助于初学者理解物质波的物理图像.

The equation for the momentum and the wavelength for the matter wave is derived in two intuitive ways.The first way is to use the Lorentz transformation to obtain the inherent time difference between the head and tail of the moving particles,and then obtain the corresponding wavelength for the material wave through its phase difference and the length of the particle occupied in space.The second way is to obtain the equation by calculating the traveling wave adapted to the phase change of the particle.These two derivation methods are intuitive and helpful to beginners to understand the physical image of the matter wave.