不确定性原理Uncertainty principle

一个空间上局域的波包必须由许多不同波长（即不同动量）的波叠加而成，位置越确定，动量分布越宽，反之亦然。从算符角度看，位置和动量算符不对易，[x̂, p̂] = iħ，不对易的可观测量不能同时取确定值。能量-时间关系 ΔE·Δt ≳ ħ/2 解释了光谱线的自然线宽：激发态寿命越短，谱线越宽。

A wave packet localised in space must be built from many wavelengths, and hence many momenta; the sharper the position, the broader the momentum distribution, and vice versa. In operator terms, position and momentum do not commute, [x̂, p̂] = iħ, and non-commuting observables cannot simultaneously have definite values. The energy–time relation ΔE·Δt ≳ ħ/2 explains the natural width of spectral lines: shorter-lived excited states give broader lines.

1927 年德国物理学家维尔纳·海森堡在哥本哈根提出这一原理，最初用“伽马射线显微镜”思想实验说明：要精确测定电子位置需用短波长光，但短波长光子会给电子很大的反冲动量。同年肯纳德给出了严格的数学形式 Δx·Δp ≥ ħ/2。海森堡因创立量子力学获 1932 年诺贝尔物理学奖。

The German physicist Werner Heisenberg proposed the principle in Copenhagen in 1927, illustrating it with a gamma-ray microscope thought experiment: locating an electron precisely requires short-wavelength light, but such photons give the electron a large recoil. Kennard gave the rigorous form Δx·Δp ≥ ħ/2 that year. Heisenberg received the 1932 Nobel Prize in Physics for creating quantum mechanics.

不确定性原理说明电子在原子中没有确定的轨迹，玻尔模型中的圆形“轨道”必须被概率性的“电子云”取代。它还解释了原子不会坍缩：电子若被限制在原子核附近，动量和动能会急剧增大。分子即使在绝对零度也有零点振动能 E₀ = ½hν，这影响同位素效应和化学平衡。

The principle means electrons in atoms have no definite trajectories, so the circular orbits of the Bohr model must give way to probabilistic electron clouds. It also explains why atoms do not collapse: confining an electron close to the nucleus would sharply raise its momentum and kinetic energy. Molecules keep a zero-point vibrational energy E₀ = ½hν even at absolute zero, which affects isotope effects and chemical equilibria.