Electro in the p A sing FIG.3:Electromagnetic Wave Propagation. o-amplitudemechanical displacement msity U哈→energy density 。Wave function 红，)=Ae(学-2）=Aetm-B Scalar wave.Amplitude-A-? Intensity-AP→ B.Wave packet-a possible way out? Two examples of localized wave packets .Superposition of waves with wave number between (o-Ak)and (+k)-square packet 因={A-AK<+as elsewhere =左 宏24恤a包 工 Amplitude Both wave number and spatial position have a spread-uncertainty relation △xπ/△k △x·△k≈T △r△p≈rh6 FIG. 3: Electromagnetic Wave Propagation. U0 − amplitude → mechanical displacement Intensity U 2 0 → energy density • Wave function ψ(x, t) = Aei( 2π λ x−2πνt) = Ae i ~ (px−Et) Scalar wave, Amplitude - A →? Intensity - A 2 →? Early attempt: Intensity → material density, particle mass distributed in wave. But wave is endless in space, how can it fit the idea of a particle which is local. B. Wave packet - a possible way out? particle = wave packet - rain drop e ik0x− an endless train, How can it be connected with particle picture? Two examples of localized wave packets • Superposition of waves with wave number between (k0 − ∆k) and (k0 + ∆k) - square packet φ(k) = { A, k0 − ∆k < k < k0 + ∆k 0, elsewhere ψ(x) = 1 √ 2π ∫ φ(k)e ikxdk = 1 √ 2π ∫ k0+∆k k0−∆k Aeikxdk = 1 √ 2π 2A sin (∆kx) x | {z } Amplitude e ik0x Both wave number and spatial position have a spread - uncertainty relation ∆x ∼ π/∆k, ∆x · ∆k ≈ π ∆x · ∆p ≈ π~