# 无限深方势阱 - Infinite Square Well

无限深方势阱中粒子的交互式可视化

> 标准页面: https://elysiatools.com/zh/visualizations/infinite-square-well

- **分类:** Physics

## 概述

Interactive visualization of particle in infinite square well potential (particle in a box). Features the fundamental quantum mechanical problem demonstrating energy quantization, wave-particle duality, zero-point energy, and the uncertainty principle. Boundary conditions: ψ(0) = ψ(a) = 0 leading to quantized energy levels Eₙ = n²π²ħ²/(2ma²) where n = 1, 2, 3, ... is the quantum number. Wave functions: ψₙ(x) = √(2/a)·sin(nπx/a) representing standing waves with n-1 nodes inside the well. Time-dependent wave function: ψₙ(x,t) = ψₙ(x)·e^(-iEₙt/ħ) showing phase evolution. Probability density: |ψₙ(x)|² = (2/a)·sin²(nπx/a) showing particle position distribution. Potential well visualization V(x) = 0 for 0 < x < a, V(x) = ∞ otherwise with infinite walls at boundaries. Real-time wave function display with real part Re[ψ] (blue) and probability density |ψ|² (purple). Energy level diagram showing first 10 quantized levels with E ∝ n² spacing. Current state highlighting with energy value display. Superposition states: single state, double state (n₁ + n₂), triple state (n₁ + n₂ + n₃) with time-dependent probability density oscillations. Wave function animation showing time evolution and phase dynamics. Node visualization showing ψ = 0 points (n-1 nodes for state n). Probability density display with gradient fill and maximum probability tracking. Expected position calculation ⟨x⟩ = ∫x|ψ|²dx. Adjustable parameters: well width a (0.5-3.0 nm), quantum number n (1-10), particle mass m (0.1-10.0 electron masses), animation speed. Quick presets: ground state (n=1), first excited (n=2), superposition state, wide well. Display options: toggle real part, probability density, nodes, grid. Educational content covers infinite square well concept, boundary conditions and quantization, wave function properties (standing waves, nodes, probability distributions), energy quantization (ground state zero-point energy, excited state spacing Eₙ ∝ n², photon transitions), superposition states and time evolution, applications (quantum dots, conjugated molecules, nuclear shell model), classical limit (n → ∞ correspondence principle with uniform probability), and fundamental quantum concepts (Heisenberg uncertainty principle, wave-particle duality). Multi-language support (zh, en, es, fr, de, ru, pt).

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