⚛️ 量子物理工具

⚛️ 光子動量計算器Photon Momentum 光子動量計算器由波長求光子的相對論動量 p=h/λ，適合光壓、康普頓散射與量子光學中的光子動量估算。Photon Momentum - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Quantum Physics tools. ⚛️ 光子能量計算器Photon Energy 光子能量計算器由頻率或波長求光子能量 E=hν=hc/λ，適合光學、原子物理與光電探測中的單光子能量換算。Photon Energy - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Quantum Physics tools. ⚛️ 光電效應計算器Photoelectric Effect 輸入入射光頻率（或波長）與金屬功函式，工具按愛因斯坦方程計算光電子最大初動能，判斷能否發生光電效應並給出截止頻率，適用於光電管與光伏原理演示。Photoelectric Effect - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Quantum Physics tools. ⚛️ 迴旋頻率計算器Cyclotron Frequency 迴旋頻率計算器求帶電粒子在勻強磁場中的迴旋角頻率 ω=qB/m，適合迴旋加速器、等離子體物理與粒子運動分析。Cyclotron Frequency - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Quantum Physics tools. ⚛️ 康普頓散射位移計算器Compton Shift 康普頓散射位移計算器求 X 射線經電子散射後的波長改變數，由散射角確定，適合康普頓效應與光子-電子相互作用分析。Compton Shift - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Quantum Physics tools. ⚛️ 德布羅意波長計算器De Broglie Wavelength 德布羅意波長計算器由動量 p 求物質波波長 λ=h/p，適合電子顯微鏡、量子力學與波粒二象性教學中的波長估算。De Broglie Wavelength - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Quantum Physics tools. ⚛️ 無限深勢阱能級計算器Infinite Well Energy 無限深勢阱能級計算器求一維方勢阱中粒子的離散能級 E_n，由勢阱寬度與質量確定，適合量子力學定態問題與教學演示。Infinite Well Energy - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Quantum Physics tools. ⚛️ 氫原子能級計算器Hydrogen Energy Level 氫原子能級計算器求第 n 能級的能量 E_n=−13.6/n² eV，適合玻爾模型、光譜與原子物理中的能級與躍遷分析。Hydrogen Energy Level - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Quantum Physics tools. ⚛️ 海森堡不確定性Heisenberg Uncertainty 海森堡不確定性計算器求位置與動量不確定度乘積的下限 Δx·Δp≥ħ/2，適合量子力學原理演示與測量極限討論。Heisenberg Uncertainty - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Quantum Physics tools. ⚛️ 玻爾軌道半徑計算器Bohr Orbit Radius 玻爾軌道半徑計算器求氫原子第 n 軌道半徑（玻爾半徑的整數平方倍），適合原子結構模型與量子物理教學演示。Bohr Orbit Radius - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Quantum Physics tools. 🔄 由主量子數求角動量Angular Momentum Quant 由主量子數求角動量工具依據 L=√(l(l+1))·ħ 或簡化 L=n·ħ 由量子數 n 求軌道角動量，適合原子物理與量子力學習題。Angular Momentum Quant - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Quantum Physics tools. ⚡ 由功率與波長求每秒光子數Photon Flux 輸入光功率 P 與波長 λ，工具按 N=P·λ/(hc) 計算每秒到達的光子數（光子通量），便於比較不同波長光源的單光子通量，用於光學探測與量子光源估算。Photon Flux - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Quantum Physics tools. ⚡ 由帶隙能量求吸收/發射波長Band Gap Photon 輸入半導體或材料的帶隙能量 E_g（電子伏特），工具按 λ=hc/E_g 計算對應的吸收或發射光子波長（奈米），便於判斷材料發光的顏色或可被何種波長光激發。Band Gap Photon - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Quantum Physics tools. 🕐 由時間不確定度求能量展寬Energy Time Uncertainty 輸入粒子存在的時間不確定度 Δt，工具按海森堡不確定性關係 ΔE≥ℏ/(2Δt) 計算最小能量展寬，說明壽命越短的狀態能級越寬，適用於激發態與自然線寬估算。Energy Time Uncertainty - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Quantum Physics tools. 🌡️ 由溫度與質量求熱德布羅意波長Thermal De Broglie 輸入粒子質量 m 與溫度 T，工具按 λ=h/√(2πmkT) 計算熱德布羅意波長，用於判斷氣體在何條件下呈現量子簡併（波長與間距相當），適用於玻色-愛因斯坦凝聚等分析。Thermal De Broglie - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Quantum Physics tools. ✂️ 由磁場求相鄰能級分裂Zeeman Splitting 輸入磁感應強度 B，工具按 ΔE=μ_B·B 計算相鄰塞曼子能級的能量差，說明外加磁場使能級等距分裂，用於原子光譜塞曼效應與磁場強度的光譜標定。Zeeman Splitting - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Quantum Physics tools. 🧲 由磁量子數求磁矩Spin Magnetic Moment 輸入軌道磁量子數 m_l，工具按 μ=μ_B·m_l 計算軌道磁矩大小（以玻爾磁子 μ_B 為單位），說明不同磁量子數對應的空間取向磁矩，用於原子磁性與塞曼效應理解。Spin Magnetic Moment - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Quantum Physics tools. 〰️ 由粒子質量求康普頓波長Compton Wavelength 由粒子質量求康普頓波長工具依據 λ_c=h/(mc) 求粒子的康普頓波長，輸入質量輸出波長，適合粒子物理與量子效應學習。Compton Wavelength - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Quantum Physics tools. 📈 由能級與頻率求能量Quantum Oscillator Energy 輸入諧振子能級量子數 n 與振動頻率 f，工具按 E_n=ℏω(n+½) 計算對應能級能量，演示量子諧振子能級等間距且存在零點能的特性，適用於分子振動與晶格聲子分析。Quantum Oscillator Energy - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Quantum Physics tools. 📊 由能級差與溫度求粒子數之比Boltzmann Population 輸入兩能級差 ΔE（eV）與絕對溫度 T，工具按玻爾茲曼分佈 N₂/N₁=exp(−ΔE/kT) 計算高能級與低能級粒子數之比，說明溫度越高高能級佔據越多，用於理解熱平衡下的布居。Boltzmann Population - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Quantum Physics tools. 📦 由自由電子密度求費米能Fermi Energy 3d 輸入自由電子數密度 n 與有效質量 m，工具按三維自由電子氣公式 E_F=(ℏ²/2m)(3π²n)^{2/3} 計算費米能，用於金屬與半導體中電子最高佔據能級的估算。Fermi Energy 3d - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Quantum Physics tools. ☀️ 由逸出功求截止頻率Photoelectric Threshold 由逸出功求截止頻率工具依據 f₀=φ/h 由金屬逸出功（eV）求光電效應截止頻率，適合光電效應與量子物理習題。Photoelectric Threshold - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Quantum Physics tools. 🔥 由面積與溫度求輻射功率Stefan Boltzmann Power 輸入黑體表面積 A 與絕對溫度 T，工具按斯特藩-玻爾茲曼定律 P=σ·A·T⁴ 計算總輻射功率，說明輻射隨溫度四次方急劇上升，用於恆星、加熱器與熱輻射估算。Stefan Boltzmann Power - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Quantum Physics tools. 📻 由頻率求電磁波波長Wavelength - Frequency Convert Calculator - Wavelength - Frequency Convert : Input f , Output λ( nm ) 由頻率求電磁波波長工具依據 λ=c/f 由頻率求波長，覆蓋射頻到光波段，適合電磁學、通訊與光學中的波長頻率換算。Wavelength - Frequency Convert Calculator - Wavelength - Frequency Convert : Input f , Output λ( nm ) - free online tool. ⚛️ 電子對產生閾能計算器Pair Production Threshold 電子對產生閾能計算器求光子產生正負電子對所需最小能量（≥2m_ec²），適合高能物理與伽馬射線與物質相互作用分析。Pair Production Threshold - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Quantum Physics tools. ⚛️ 維恩位移定律計算器Wien Displacement 維恩位移定律計算器求黑體輻射峰值波長與溫度的反比關係 λ_max·T=b，適合熱輻射、恆星溫度估算與紅外物理學習。Wien Displacement - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Quantum Physics tools. ⚛️ 質能等價計算器Mass Energy Equivalence 質能等價（E=mc²）線上計算器，輸入質量求得對應能量，或反向由能量求質量，用於核物理與相對論教學，純前端。Mass Energy Equivalence - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Quantum Physics tools. ⚛️ 裡德伯波長計算器Rydberg Wavelength 裡德伯波長計算器求氫原子譜線波長（由初末能級與裡德伯常數確定），適合巴爾末系等發射/吸收光譜的波長推算。Rydberg Wavelength - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Quantum Physics tools.