Quantum Mechanics
🌊 Wave-Particle Duality
Matter and radiation exhibit both wave-like and particle-like properties simultaneously. Electron single-particle interference verifies the de Broglie relation.
λ = h/p , E = hν❓ Uncertainty Principle
Position and momentum cannot be precisely determined simultaneously. Heisenberg uncertainty is an intrinsic limitation of the quantum world.
Δx · Δp ≥ ℏ/2🎲 Quantum Superposition
A system can exist in a linear superposition of multiple eigenstates. The probability of obtaining a particular measurement result is determined by the squared amplitude.
|ψ⟩ = α|0⟩ + β|1⟩🧲 Quantum Tunneling
Particles have a probability of tunneling through barriers higher than their own energy. Forbidden in classical mechanics, this is prevalent in the quantum world.
T ≈ exp(-2κd)Interactive Experiment Zone
Switch modes, adjust parameters, observe quantum effects📘 From Classical to Quantum
In the double-slit experiment, individual particles exhibit interference fringes, indicating that particles "pass through both slits simultaneously". Once path information is detected, interference disappears. Measurement irreversibly changes the system state.
📊 Probability Interpretation
The squared modulus of the wave function |ψ|² gives the probability density. Bright fringes on the screen correspond to high-probability regions, dark fringes to low probability. Quantum mechanics predicts statistical distributions, not individual outcomes.
🔬 Real-world Applications
Scanning Tunneling Microscopy (STM) is based on quantum tunneling. Quantum computers utilize superposition and entanglement. Semiconductor physics relies on band theory and uncertainty principles.