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量子物理
12
engines
de Broglie wavelength · matter waves
de Broglie wavelength · matter waves
λ=h/p=h/mv · 物质波 · 电子100eV→123pm
Every particle is also a wave: λ = h/(mv)
Heisenberg uncertainty · Δx·Δp ≥ ℏ/2
Heisenberg uncertainty · Δx·Δp ≥ ℏ/2
Δx·Δp≥ℏ/2 · 位置-动量权衡 · 波包展宽
Pinning down position blurs momentum, and vice versa
Wave–particle duality · double slit
Wave–particle duality · double slit
双缝干涉 · 条纹间距 Δy=λL/d · 单粒子累积
Two slits, one screen: interference from d·sinθ = mλ
Quantum tunneling
Quantum tunneling
势垒穿透 T≈e^(−2κa) · κ=√(2m(V−E))/ℏ · 指数衰减
Transmission through a rectangular potential barrier · exact κ and T
Quantum harmonic oscillator
Quantum harmonic oscillator
E_n=ℏω(n+½) · 等间距能级 · 零点能 ½ℏω
Equally-spaced energy levels E_n = ℏω(n+½) · zero-point energy · |ψ_n|²
Compton scattering
Compton scattering
Δλ=(h/m_ec)(1−cosθ) · 康普顿波长 2.426pm · 反冲电子
Wavelength shift Δλ = (h/m_e c)(1 − cosθ), Compton wavelength = 2.426 pm
Bloch sphere · single qubit
Bloch sphere · single qubit
|ψ⟩=cos(θ/2)|0⟩+e^iφsin(θ/2)|1⟩ · P=cos²(θ/2)
A qubit state |ψ⟩ = cos(θ/2)|0⟩ + e^(iφ)·sin(θ/2)|1⟩ as a point on the sphere
Stern–Gerlach · spin quantization
Stern–Gerlach · spin quantization
自旋½量子化 · 二分裂 · 序列分析器 cos²(Δ/2)
A spin-½ beam splits into exactly two branches, not a continuum
Bell / CHSH · quantum entanglement
Bell / CHSH · quantum entanglement
E(a,b)=−cos(a−b) · CHSH S≤2 vs 2√2≈2.828
Correlations of an entangled pair violate the classical bound S ≤ 2
Pair production · γ → e⁺ + e⁻
Pair production · γ → e⁺ + e⁻
γ→e⁺e⁻ · 阈值 2m_ec²=1.022 MeV · 湮灭 0.511 MeV
A high-energy photon near a nucleus converts into an electron–positron pair
Mass–energy equivalence · E = γmc²
Mass–energy equivalence · E = γmc²
E=γmc² · 相对论动能 (γ−1)mc² · E²=(pc)²+(mc²)²
Rest energy, Lorentz factor, relativistic vs classical kinetic energy
Normal Zeeman effect · magnetic splitting
Normal Zeeman effect · magnetic splitting
ΔE=m_l·μ_B·B · 2l+1 子能级 · Δν=μ_B·B/h
A magnetic field splits one level into 2l+1 sublevels and a spectral line into a triplet