--- title: "少掉的氢原子怎样暴露了 Lamb 位移" description: "一个下游信号的凹陷，怎样指出氢原子理论里漏掉的能量？" canonical_url: "https://sandboxphysics.com/zh/stories/quantum-evidence/lamb-shift-microwave-evidence/" language: "zh-CN" page_type: "story" alternate_languages: en: "https://sandboxphysics.com/stories/quantum-evidence/lamb-shift-microwave-evidence/" last_modified: "2026-10-24" --- [量子物理：读懂证据](https://sandboxphysics.com/zh/stories/quantum-evidence/) 诺奖 A · 证据与操控 # 少掉的氢原子怎样暴露了 Lamb 位移 Sandbox Physics · 2026-10-15 一个下游信号的凹陷，怎样指出氢原子理论里漏掉的能量？ ## 理论里重合的两个能级 1947 年，Lamb 和 Retherford 用微波研究氢原子，发现两个按理应当重合的激发能级，实际上隔着一小段能量。其中的 S 态比 P 态高，间隔对应约一吉赫兹，也就是每秒十亿次振荡的微波。 这对当时成功的 Dirac 氢原子理论是一个明确的问题。理论已经解释了许多精细的谱线结构，却把这两个态放在同一能量上。实验要分清的正是这一小段差额。 证据阅读：W. E. Lamb Jr. and R. C. Retherford (1947), Fine Structure of the Hydrogen Atom by a Microwave Method Lamb and Retherford (1947), original paper scan hosted by the University of Maryland, pp. 241–243 ## 让活得久的原子报告一次跃迁 原子束中有一部分氢原子处在亚稳态：它们受了激发，却能保持相当长的时间，足够飞到下游。撞上金属靶时，它们会释放出可探测的电子，形成电流。 另一种相关激发态寿命很短。微波把长寿命原子转到短寿命态，它就会很快衰变。飞到靶上时，它已经失去原来的身份，电流也就少一份。把难以直接看清的能级变化，换成存活原子数目的变化，便有了可读的共振信号。 早期报告固定微波频率，改变磁场，记录电流怎样随之下降。磁场调节能级间隔，直到它与微波匹配。下游电流的谷，标出了原子容易被转走的位置。 证据阅读：Lamb and Retherford (1947), original paper scan hosted by the University of Maryland, pp. 241–243 ## 从磁场中的跃迁，推回零磁场的差额 观测到的跃迁随磁场变化，研究者再从这些关系推断两个能级在零磁场下相隔多少。通常所说的正 Lamb 位移定义如下：两个符号分别标记第二层的 S 态和 P 态，h 是普朗克常数，频率乘以它就是能量差。这里已经把相应的结构区分开。 原论文给的是约一吉赫兹的初步结果。图注特意说明，画出的平移比较曲线并非最佳拟合。短寿命态的自然宽度、超精细结构、较强微波以及磁场不均匀，都会把谷形展宽；磁场标定也限制了结果的精度。 $$ h\nu_{\mathrm L}=E(2S_{1/2})-E(2P_{1/2}) $$ 证据阅读：Lamb and Retherford (1947), original paper scan hosted by the University of Maryland, pp. 241–243 ## 原子还要和电磁场一起计算 Bethe 在同年给出了电磁相互作用引起能级位移的理论计算。电子处在原子里，也与电磁场相互作用；理想 Dirac–Coulomb 模型没有计入的影响，终于在这段极小的能量差中显出来。 这推动了量子电动力学的发展，也给后来的精密比较留下了目标：测量和计算都要逐项处理更小的效应。1947 年的实验首先清楚地指出，两个本应重合的能级需要分开。那条少了原子的电流曲线，把理论需要补上的地方标了出来。 证据阅读：H. A. Bethe (1947), The Electromagnetic Shift of Energy Levels, Phys. Rev. 72, 339 Lamb and Retherford (1947), original paper scan hosted by the University of Maryland, pp. 241–243 ## 接着操作模型 下面这些教学 Lab 产生的是模拟数据，和上文讨论的历史观测不是一回事。 - [从模拟的存活原子计数找微波共振](https://sandboxphysics.com/zh/labs/lamb-shift-microwave/) - [对照加入 Lamb 修正以前的氢原子能级](https://sandboxphysics.com/zh/labs/hydrogen-orbitals-spectra/) ## 来源与阅读说明 1947 年 Lamb–Retherford 论文读的是马里兰大学保存的扫描本，包括信号方法和图注。论文给出的约一吉赫兹初步结果，与后来的精密数值分开叙述。Bethe 的论文是理论上的跟进，不是又一次实验。 1. [W. E. Lamb Jr. and R. C. Retherford (1947), Fine Structure of the Hydrogen Atom by a Microwave Method](https://doi.org/10.1103/PhysRev.72.241) 2. [Lamb and Retherford (1947), original paper scan hosted by the University of Maryland, pp. 241–243](https://physics.umd.edu/grt/taj/624b/Lamb1947.pdf) 3. [H. A. Bethe (1947), The Electromagnetic Shift of Energy Levels, Phys. 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