▼ (Click To View) ▼▼ (Tap To View) ▼

∇μFμν=μ₀Jν ∂μF̃μν=0 Rμν−½Rgμν+Λgμν=(8πG/c⁴)Tμν iℏ∂ψ/∂t=Ĥψ Ĥ=−(ℏ²/2m)∇²+V(x,t) E²=p²c²+m²c⁴ ΔxΔp≥ℏ/2 S=kBlnΩ Z=Σᵢe^(−βEᵢ) F=−kBTlnZ ∂ρ/∂t+(i/ℏ)[Ĥ,ρ]=0 □φ+(m²c²/ℏ²)φ=0 (iγμ∂μ−mc/ℏ)ψ=0 [x̂,p̂]=iℏ ⟨A⟩=⟨ψ|Â|ψ⟩ ∮p·dq=nh Γμνλ=½gλσ(∂μgσν+∂νgσμ−∂σgμν) Rρσμν=∂μΓρνσ−∂νΓρμσ+ΓρμλΓλνσ−ΓρνλΓλμσ Gμν=Rμν−½Rgμν δS=0 S=∫ℒ√(−g)d⁴x ℒ=ψ̄(iℏcγμDμ−mc²)ψ−¼FμνFμν Dμ=∂μ+igAμ ψ(x,t)=∫φ(k)e^[i(k·x−ωt)]d³k ω²=c²k²+(mc²/ℏ)² E=ℏω p=ℏk λ=h/p α=e²/(4πε₀ℏc)≈1/137.036 ΔEΔt≳ℏ/2 ∂S/∂t+H(q,∂S/∂q,t)=0 d²xμ/dτ²+Γμ αβ(dxα/dτ)(dxβ/dτ)=0 ds²=gμνdxμdxν P(x)=|ψ(x)|² Tr(ρ)=1 ρ²=ρ⇒pure det(M−λI)=0 ∇·E=ρ/ε₀ ∇·B=0 ∇×E=−∂B/∂t ∇×B=μ₀J+μ₀ε₀∂E/∂t c=1/√(μ₀ε₀) E=mc² τ=ℏ/(ΔE) λC=ℏ/(mc) rₛ=2GM/c² T_H=ℏc³/(8πGMkB) S_BH=kBc³A/(4Gℏ) H²=(8πG/3)ρ−kc²/a²+Λc²/3 ẋ=aH Ω=ρ/ρc ρc=3H²/(8πG) ∫𝒟φ e^(iS[φ]/ℏ) det(γμpμ−mc)=0 SU(3)×SU(2)×U(1) Q=T₃+Y/2 β(g)=μ∂g/∂μ ζ(s)=Σₙ₌₁∞n^(−s) e^(iπ)+1=0 ∫₋∞∞e^(−x²)dx=√π limₙ→∞(1+1/n)ⁿ=e Σₙ₌₁∞1/n²=π²/6 Γ(z)=∫₀∞t^(z−1)e^(−t)dt ∂²u/∂t²=c²∇²u ∇²Φ=4πGρ δ⁴(x−x′) □G(x−x′)=−δ⁴(x−x′) Ψ=Σₙcₙ|n⟩ Σₙ|cₙ|²=1 [Jᵢ,Jⱼ]=iℏεᵢⱼₖJₖ ΔS_universe≥0 t_P=√(ℏG/c⁵) ℓ_P=√(ℏG/c³) m_P=√(ℏc/G) ρΛ=Λc²/(8πG) QED⊂SU(3)×SU(2)×U(1) ∂μTμν=0 ∇μGμν=0 e^(−iĤt/ℏ)|ψ(0)⟩=|ψ(t)⟩ ∫|ψ|²d³x=1 Ω=e^(S/kB) δ(√−g R)/δgμν=√−g(Rμν−½Rgμν) ∂ℒ/∂φ−∂μ(∂ℒ/∂(∂μφ))=0 ħ=c=G=1 ⇒ S=A/4