M N AkAx 1 FIG.4:Wave packet formed by plane waves with different frequency. Plane wave:lk /ave packet:ko and FIG.5:Spread of a wave packet Both wave number and spatial position have a spread-uncertainty relation △x~T/△k, △x·△k≈T △x·△p≈rh .Superposition of waves with wave number in a Gaussian packet =(） e-a(k-bo)2 Problem 1 The Fourier transformation of(k)is also Gaussian.It is the best one can do to localize a particle in position and momentum spaces at the same time.Find the root mean square(RMS)deviation△x·△p=? 10 FIG. 4: Wave packet formed by plane waves with different frequency. FIG. 5: Spread of a wave packet. Both wave number and spatial position have a spread - uncertainty relation ∆x ∼ π/∆k, ∆x · ∆k ≈ π ∆x · ∆p ≈ π~ • Superposition of waves with wave number in a Gaussian packet ϕ(k) = µ 2α π ¶1/4 e −α(k−k0) 2 Problem 1 The Fourier transformation of ϕ(k) is also Gaussian. It is the best one can do to localize a particle in position and momentum spaces at the same time. Find the root mean square (RMS) deviation ∆x · ∆p =? 10