# 量子隧穿 - Quantum Tunneling

展示量子隧穿效应通过势垒的交互式可视化

> 标准页面: https://elysiatools.com/zh/visualizations/quantum-tunneling

- **分类:** Physics

## 概述

Interactive visualization of quantum tunneling effect through potential barriers. Features the fundamental quantum mechanical phenomenon where particles can pass through barriers even when energy E < barrier height V₀. Three-region analysis: Region I (x < 0): ψ = Ae^(ikx) + Be^(-ikx) with incident and reflected waves, Region II (0 ≤ x ≤ a): ψ = Ce^(κx) + De^(-κx) showing exponential decay, Region III (x > a): ψ = Fe^(ikx) representing transmitted wave. Key equations: wave number k = √(2mE)/ħ, decay constant κ = √[2m(V₀-E)]/ħ, transmission coefficient T ≈ e^(-2κa), reflection coefficient R = 1 - T. Potential barrier visualization showing rectangular barrier with adjustable parameters. Real-time wave function display with real part Re[ψ] (blue), imaginary part Im[ψ] (green), and probability density |ψ|² (purple). Wave packet animation using Gaussian envelope showing incident packet approaching barrier, partial transmission and reflection. Probability bars displaying transmission probability T (%) and reflection probability R (%). Classical vs quantum comparison: classical particles reflect when E < V₀, quantum particles have non-zero tunneling probability. Adjustable parameters: particle energy E (0.1-2.0 eV), barrier height V₀ (0.2-3.0 eV), barrier width a (0.2-3.0 nm), particle mass m (0.1-5.0 electron masses), wave packet width σ (0.2-1.5 nm). Quick presets: electron (m=1me), proton (m=1836me), high tunneling (thin barrier), low tunneling (thick barrier). Display options: toggle real/imaginary parts, probability density, region labels (I, II, III). Educational content covers quantum tunneling concept, wave-particle duality explanation, exponential barrier penetration, key factors affecting tunneling (energy, barrier height/width, particle mass), applications: scanning tunneling microscope (STM, 1986 Nobel Prize), flash memory, nuclear fusion in stars (proton tunneling through Coulomb barrier), alpha decay, tunnel diodes, and classical limit for macroscopic objects. Multi-language support (zh, en, es, fr, de, ru, pt).

## 相关内容

- [零级反应 - Zero-Order Reaction](https://elysiatools.com/zh/visualizations/zero-order-reaction): 零级反应动力学和浓度随时间变化的交互式可视化
- [一级反应 - First-Order Reaction](https://elysiatools.com/zh/visualizations/first-order-reaction): 一级反应动力学和指数浓度衰减的交互式可视化
- [二级反应 - Second-Order Reaction](https://elysiatools.com/zh/visualizations/second-order-reaction): 二级反应动力学和双分子碰撞动力学的交互式可视化
- [阿伦尼乌斯方程 - Arrhenius Equation](https://elysiatools.com/zh/visualizations/arrhenius-equation): 温度对反应速率影响的交互式可视化 - 探索活化能、指数因子和速率常数的关系
- [可逆反应 - Reversible Reaction](https://elysiatools.com/zh/visualizations/reversible-reaction): A ⇌ B 可逆反应动力学的交互式可视化 - 探索正逆反应速率、平衡常数和浓度随时间的变化
- [连续反应 - Consecutive Reaction](https://elysiatools.com/zh/visualizations/consecutive-reaction): A → B → C 连续反应动力学的交互式可视化 - 探索中间物浓度峰值、决速步和所有物种的完整演化
- [链式反应 - Chain Reaction](https://elysiatools.com/zh/visualizations/chain-reaction): 自由基链式反应聚合的交互式可视化 - 探索引发、增长、终止步骤，链增长动画和分子量分布
- [勒夏特列原理 - Le Chatelier's Principle](https://elysiatools.com/zh/visualizations/le-chateliers-principle): 勒夏特列原理的交互式可视化 - 探索浓度、压强和温度变化如何影响化学平衡，配合分子动力学动画展示平衡移动过程