德布罗意波Matter wave

德布罗意认为既然光同时具有波和粒子的性质，那么电子等实物粒子也应如此，并把光子的 p = h/λ 推广到所有粒子。宏观物体由于质量大，波长极短而无法观察（一颗以 30 m/s 飞行的 0.15 kg 棒球波长约 10⁻³⁴ m）；电子质量小，波长与原子间距相当，因此能被晶体衍射。玻尔轨道的量子化条件可以理解为电子驻波：轨道周长必须等于波长的整数倍，2πr = nλ。

De Broglie reasoned that if light is both wave and particle, so too should be electrons and other matter, and he extended the photon relation p = h/λ to all particles. Massive everyday objects have unobservably short wavelengths (a 0.15 kg baseball at 30 m/s has about 10⁻³⁴ m), but electrons are light enough to have wavelengths comparable to atomic spacings and are diffracted by crystals. Bohr's quantisation condition can be read as a standing-wave condition: the orbit circumference must be a whole number of wavelengths, 2πr = nλ.

1924 年法国物理学家路易·德布罗意在博士论文中提出物质波假说，答辩委员会把论文送给爱因斯坦，爱因斯坦给予高度评价。1927 年戴维森-革末实验和 G. P. 汤姆孙实验观测到电子衍射。德布罗意因此获 1929 年诺贝尔物理学奖，这是首次因博士论文成果获奖。

In 1924 the French physicist Louis de Broglie proposed matter waves in his doctoral thesis; the examiners sent it to Einstein, who praised it highly. The Davisson–Germer and G. P. Thomson experiments observed electron diffraction in 1927, and de Broglie received the 1929 Nobel Prize in Physics, the first award for work from a doctoral thesis.

电子显微镜利用高能电子极短的德布罗意波长（200 kV 电子约 2.5 pm）实现原子分辨率成像；低能电子衍射（LEED）研究晶体表面结构；中子衍射用于测定晶体中氢原子位置和磁结构；原子干涉仪用于精密测量重力加速度。

Electron microscopes exploit the tiny de Broglie wavelength of fast electrons (about 2.5 pm at 200 kV) for atomic-resolution imaging; low-energy electron diffraction (LEED) probes crystal surfaces; neutron diffraction locates hydrogen atoms and magnetic structures in crystals; and atom interferometers measure gravitational acceleration precisely.