Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

10.101 Davisson-Germer 电子衍射的几何复现

guobin ouyang

Published Sep 12, 2026• 0 citations
Publisher

Abstract

Davisson-Germer 实验是物质波最直接的经典证据之一。本文先从 10.98 的电子锚生成 54 eV 电子的德布罗意波长,再把镍晶体作为周期性散射坐标卡,计算 Ni(111) 晶面的一级布拉格散射角。随后在同一个前向模型中加入束能分布、探测器角度映射、FCC 运动学结构因子、低能电子势限界、一阶 Darwin 多次散射和热漫散射权重。 几何输入仍给出: $$ \lambda_e(54\,\mathrm{eV}) =1.668707\times10^{-10}\,\mathrm{m}, $$ $$ d_{111}=\frac{a_{\mathrm{Ni}}}{\sqrt{3}} =2.034582\times10^{-10}\,\mathrm{m}, $$ $$ \Theta_{\mathrm{geo}} =2\arcsin\left(\frac{\lambda_e}{2d_{111}}\right) =48.420470^\circ. $$ 相对历史宽窗中心 $50^\circ$,几何峰位低 $1.579530^\circ$,即 $$ \frac{\Theta_{\mathrm{geo}}-\Theta_{\mathrm{hist}}} {\Theta_{\mathrm{hist}}} =-3.1591\times10^{-2}, \qquad \frac{|\Theta_{\mathrm{geo}}-\Theta_{\mathrm{hist}}|} {\sigma_{\mathrm{broad}}} =0.7898, $$ 其中 $\sigma_{\mathrm{broad}}=2^\circ$ 只是审计半宽,不是现代实验给出的高斯标准差。 第一轮已得到三项有限闭合: 1. 在 $T_c=1100\,\mathrm{K}$ 和仪器能量高斯宽度 $\sigma_I=0.10\,\mathrm{eV}$ 下,54 eV 束能卷积给出的 Ni(111) 本征角宽为 $0.136^\circ$,加入探测器角点扩散宽度 $0.20^\circ$ 后为 $0.494^\circ$; 2. 在显式探测器参数箱内,一级峰的可达观察区间为 $[48.138480^\circ,48.702460^\circ]$,历史中心 $50^\circ$ 仍在区间外 $1.297540^\circ$; 3. FCC 运动学结构因子与温度依赖 Debye-Waller 权重给出 Ni(200)/Ni(111) 相对权重 $0.771269$,替代了原先没有晶格依据的现象学包络。 第二轮再完成三项有限闭合: 4. Wentzel 屏蔽库仑势给出 54 eV Ni(111) 电子形状因子区间,并将其与 Mott-Bethe 高能极限及几何真空波长链分开; 5. 一阶 Darwin 层散射包络给出相对运动学强度的修正区间 $[0.288314,2.140518]$,对应 $-71.169\%$ 至 $+114.052\%$; 6. Debye 模型给出 $300\,\mathrm{K}$ 时 $B_{\mathrm{Ni}}=0.3077604\,\mathrm{\mathring{A}}^2$、Ni(111) 零声子强度 $0.963509$ 和热漫散射权重 $0.0364909$。 第三轮再得到两项条件闭合: 7. 12 层 Darwin 审计和对第一、第二层弛豫、缺陷衰减和共同相位的标准化 Jacobian 秩为 $3$,三个奇异值为 $[0.983839,0.358634,0.002943]$;共同相位构成严格零空间,第一、第二层弛豫只在很弱的奇异方向上可组合辨识; 8. 声子分辨热漫散射的角度判别比为 $54.0834$,能量尺度与当前束能分辨率之比为 $0.281434<1$,后者给出能量分辨 no-go;理想 Poisson 条件下全局和峰区 $5\sigma$ 计数门槛分别为 $685.101$ 和 $20956.6$。 这些结果把表面低阶可辨识界面和热漫散射测量门槛写成可审计条件,但没有把标准 LEED 层矩阵或声子核冒充为几何论独立预言。完整 LEED 动力学解、单温度下热耗损与静态缺陷的分离、真实光学势相位、历史探测器独立标定和独立 Ni 晶格输出仍然开放。 ---

DOI
10.5281/zenodo.22723268

Related papers

Davisson—Germer Experiment

Friedel Weinert

Compendium of Quantum Physics•Jan 1, 2009•5 citations

Davisson-Germer Experiment, Another Interpretation

Alfred Phillips

APS•Mar 1, 2002•0 citations

Wrong interpretation of Davisson & Germer

Kanay Barik

International Journal of Scientific Research•Jun 1, 2012•0 citations

10.71 几何退相干:V-D 互补恒等式与信息场衰减

guobin ouyang

本文攻取离散随机家族覆盖审核的第 5 项缺口(量子退相干机制),给出两个结果: 1. **静态互补恒等式(纯代数,A0 类,可提交主库)**:对双通道投影强度 σ₁、σ₂(#257 归一化 σ₁+σ₂=1),干涉可见度 V = 2√(σ₁σ₂)/(σ₁+σ₂)(10.61 推论 10.61.3.03)与路径不平衡度 D = |σ₁−σ₂|/(σ₁+σ₂) 满足 $$V^2 + D^2 = 1.$$ 这是量子信息中 Englert 对偶关系(D²+V² ≤ 1)在纯态双缝几何中的精确等号形式——干涉清晰度与路径可分辨度是单位圆上的两个互补坐标。注意 V 与 D 由同一对投影强度 (σ₁,σ₂) 定义,V²+D²=1 是归一化 σ₁+σ₂=1 的代数恒等式(形式对应,非两个独立结构的偶然相遇)。 2. **退相干动力学(中间层构造)**:环境印记重叠按信息场衰减率衰减(5.1 定理 5.1.2.01,Γ_geo = μ₁/N_info = 0.02308625),⟹ 可见度指数衰减 $$V(t) = V_0 e^{-\Gamma_{\text{geo}} t}, \qquad \tau_{\text{dec}} = 1/\Gamma_{\text{geo}} = 43.32 \ \text{编码步}, \qquad t_{1/2} = 30.02.$$ 5.1 §2 早已列出的"信息场衰减 vs 量子退相干"类比表(e^{−Γ_geo t} vs e^{−t/T₂})在此获得定量定理形式(衰减率 Γ_geo 为构造锚定,见 §5)。 **关键依赖**:5.1 定理 5.1.2.01(信息场衰减定理)、10.61 推论 10.61.3.03(对比度公式)、10.61 命题 10.61.2.02(等权重归一化);#257(扇区权重归一化)、#259(Born 法则代数形式 Δλᵢ = K√σᵢ);10.70 定理 10.70.3.01(几何 Zeno 冻结,关联对比)。 ---

•Sep 9, 2026•0 citations

On the polarisation of electrons by scattering

E. G. Dymond

Abstract The possibility of demonstrating the spin of the electron directly has been discussed since the first growth of wave mechanical conceptions, and the ascription of a magnetic moment to the electron to explain doubling of spectral lines. Bohr has shown, however, that any experiment designed to do this by deflection in a magnetic field, in any manner similar to that used by Gerlach and Stem to measure the magnetic moment of atoms, must fail owing to the operation of the Uncertainty Principle. It does not seem, however, that this will hinder us from demonstrating an asymmetry in the electron by means of scattering experiments; the method is closely analogous to the asymmetric scattering of polarised light, and was in fact used by Barkla to show the polarisation of X-rays. The earlier experiments which were carried out on the polarisation of electrons by Wolf, by Joffé and Arsenieva and by Davisson and Germer all led to negative results. The very careful work of Davisson and Germer should be specially mentioned, in that they reflected electrons from the faces of single crystals at angles corresponding to coherent scattering of the waves. Working up to a velocity of 120 volts they found no asymmetry in the scattering more than ½ per cent., which was within the limit of error of the apparatus. Darwin has shown, however, that no polarisation is to be expected in this type of experiment.

Proceedings of the Royal Society of London Series A Containing Papers of a Mathematical and Physical Character•Jun 1, 1932•19 citations

Davisson-Germer ; Difração de elétrons de Davisson-Germer

Sarah B. McKagan, Carl Wieman, Kathy Perkins +1 more

•Jan 1, 2008•0 citations
Davisson-Germer 实验是物质波最直接的经典证据之一。本文先从 10.98 的电子锚生成 54 eV 电子的德布罗意波长,再把镍晶体作为周期性散射坐标卡,计算 Ni(111) 晶面的一级布拉格散射角。随后在同一个前向模型中加入束能分布、探测器角度映射、FCC 运动学结构因子、低能电子势限界、一阶 Darwin 多次散射和热漫散射权重。 几何输入仍给出: λe(54 eV)=1.668707×10−10 m,\lambda_e(54\,\mathrm{eV}) =1.668707\times10^{-10}\,\mathrm{m},λe​(54eV)=1.668707×10−10m, d111=aNi3=2.034582×10−10 m,d_{111}=\frac{a_{\mathrm{Ni}}}{\sqrt{3}} =2.034582\times10^{-10}\,\mathrm{m},d111​=3​aNi​​=2.034582×10−10m, Θgeo=2arcsin⁡(λe2d111)=48.420470∘.\Theta_{\mathrm{geo}} =2\arcsin\left(\frac{\lambda_e}{2d_{111}}\right) =48.420470^\circ.Θgeo​=2arcsin(2d111​λe​​)=48.420470∘. 相对历史宽窗中心 50∘50^\circ50∘,几何峰位低 1.579530∘1.579530^\circ1.579530∘,即 Θgeo−ΘhistΘhist=−3.1591×10−2,∣Θgeo−Θhist∣σbroad=0.7898,\frac{\Theta_{\mathrm{geo}}-\Theta_{\mathrm{hist}}} {\Theta_{\mathrm{hist}}} =-3.1591\times10^{-2}, \qquad \frac{|\Theta_{\mathrm{geo}}-\Theta_{\mathrm{hist}}|} {\sigma_{\mathrm{broad}}} =0.7898,Θhist​Θgeo​−Θhist​​=−3.1591×10−2,σbroad​∣Θgeo​−Θhist​∣​=0.7898, 其中 σbroad=2∘\sigma_{\mathrm{broad}}=2^\circσbroad​=2∘ 只是审计半宽,不是现代实验给出的高斯标准差。 第一轮已得到三项有限闭合: 1. 在 Tc=1100 KT_c=1100\,\mathrm{K}Tc​=1100K 和仪器能量高斯宽度 σI=0.10 eV\sigma_I=0.10\,\mathrm{eV}σI​=0.10eV 下,54 eV 束能卷积给出的 Ni(111) 本征角宽为 0.136∘0.136^\circ0.136∘,加入探测器角点扩散宽度 0.20∘0.20^\circ0.20∘ 后为 0.494∘0.494^\circ0.494∘; 2. 在显式探测器参数箱内,一级峰的可达观察区间为 [48.138480∘,48.702460∘][48.138480^\circ,48.702460^\circ][48.138480∘,48.702460∘],历史中心 50∘50^\circ50∘ 仍在区间外 1.297540∘1.297540^\circ1.297540∘; 3. FCC 运动学结构因子与温度依赖 Debye-Waller 权重给出 Ni(200)/Ni(111) 相对权重 0.7712690.7712690.771269,替代了原先没有晶格依据的现象学包络。 第二轮再完成三项有限闭合: 4. Wentzel 屏蔽库仑势给出 54 eV Ni(111) 电子形状因子区间,并将其与 Mott-Bethe 高能极限及几何真空波长链分开; 5. 一阶 Darwin 层散射包络给出相对运动学强度的修正区间 [0.288314,2.140518][0.288314,2.140518][0.288314,2.140518],对应 −71.169%-71.169\%−71.169% 至 +114.052%+114.052\%+114.052%; 6. Debye 模型给出 300 K300\,\mathrm{K}300K 时 BNi=0.3077604 A˚2B_{\mathrm{Ni}}=0.3077604\,\mathrm{\mathring{A}}^2BNi​=0.3077604A˚2、Ni(111) 零声子强度 0.9635090.9635090.963509 和热漫散射权重 0.03649090.03649090.0364909。 第三轮再得到两项条件闭合: 7. 12 层 Darwin 审计和对第一、第二层弛豫、缺陷衰减和共同相位的标准化 Jacobian 秩为 333,三个奇异值为 [0.983839,0.358634,0.002943][0.983839,0.358634,0.002943][0.983839,0.358634,0.002943];共同相位构成严格零空间,第一、第二层弛豫只在很弱的奇异方向上可组合辨识; 8. 声子分辨热漫散射的角度判别比为 54.083454.083454.0834,能量尺度与当前束能分辨率之比为 0.281434<10.281434<10.281434<1,后者给出能量分辨 no-go;理想 Poisson 条件下全局和峰区 5σ5\sigma5σ 计数门槛分别为 685.101685.101685.101 和 20956.620956.620956.6。 这些结果把表面低阶可辨识界面和热漫散射测量门槛写成可审计条件,但没有把标准 LEED 层矩阵或声子核冒充为几何论独立预言。完整 LEED 动力学解、单温度下热耗损与静态缺陷的分离、真实光学势相位、历史探测器独立标定和独立 Ni 晶格输出仍然开放。 ---
本文攻取离散随机家族覆盖审核的第 5 项缺口(量子退相干机制),给出两个结果: 1. **静态互补恒等式(纯代数,A0 类,可提交主库)**:对双通道投影强度 σ₁、σ₂(#257 归一化 σ₁+σ₂=1),干涉可见度 V = 2√(σ₁σ₂)/(σ₁+σ₂)(10.61 推论 10.61.3.03)与路径不平衡度 D = |σ₁−σ₂|/(σ₁+σ₂) 满足 V2+D2=1.V^2 + D^2 = 1.V2+D2=1. 这是量子信息中 Englert 对偶关系(D²+V² ≤ 1)在纯态双缝几何中的精确等号形式——干涉清晰度与路径可分辨度是单位圆上的两个互补坐标。注意 V 与 D 由同一对投影强度 (σ₁,σ₂) 定义,V²+D²=1 是归一化 σ₁+σ₂=1 的代数恒等式(形式对应,非两个独立结构的偶然相遇)。 2. **退相干动力学(中间层构造)**:环境印记重叠按信息场衰减率衰减(5.1 定理 5.1.2.01,Γ_geo = μ₁/N_info = 0.02308625),⟹ 可见度指数衰减 V(t)=V0e−Γgeot,τdec=1/Γgeo=43.32 编码步,t1/2=30.02.V(t) = V_0 e^{-\Gamma_{\text{geo}} t}, \qquad \tau_{\text{dec}} = 1/\Gamma_{\text{geo}} = 43.32 \ \text{编码步}, \qquad t_{1/2} = 30.02.V(t)=V0​e−Γgeo​t,τdec​=1/Γgeo​=43.32 编码步,t1/2​=30.02. 5.1 §2 早已列出的"信息场衰减 vs 量子退相干"类比表(e^{−Γ_geo t} vs e^{−t/T₂})在此获得定量定理形式(衰减率 Γ_geo 为构造锚定,见 §5)。 **关键依赖**:5.1 定理 5.1.2.01(信息场衰减定理)、10.61 推论 10.61.3.03(对比度公式)、10.61 命题 10.61.2.02(等权重归一化);#257(扇区权重归一化)、#259(Born 法则代数形式 Δλᵢ = K√σᵢ);10.70 定理 10.70.3.01(几何 Zeno 冻结,关联对比)。 ---
Abstract The possibility of demonstrating the spin of the electron directly has been discussed since the first growth of wave mechanical conceptions, and the ascription of a magnetic moment to the electron to explain doubling of spectral lines. Bohr has shown, however, that any experiment designed to do this by deflection in a magnetic field, in any manner similar to that used by Gerlach and Stem to measure the magnetic moment of atoms, must fail owing to the operation of the Uncertainty Principle. It does not seem, however, that this will hinder us from demonstrating an asymmetry in the electron by means of scattering experiments; the method is closely analogous to the asymmetric scattering of polarised light, and was in fact used by Barkla to show the polarisation of X-rays. The earlier experiments which were carried out on the polarisation of electrons by Wolf, by Joffé and Arsenieva and by Davisson and Germer all led to negative results. The very careful work of Davisson and Germer should be specially mentioned, in that they reflected electrons from the faces of single crystals at angles corresponding to coherent scattering of the waves. Working up to a velocity of 120 volts they found no asymmetry in the scattering more than ½ per cent., which was within the limit of error of the apparatus. Darwin has shown, however, that no polarisation is to be expected in this type of experiment.