Problem 2 (20 points) The state of a particle in one-dimension is described by the following wavefunc- tion: V(x) = Cexp Poz 2a2 where po, To and a are real parameters. 1. Find and plot the probability distribution for the particle coordinates (for the plot, choose ro = 0.5 m, po = 10 kg m/s and a = 1 m) 2. Find and plot the probability distribution for the particle momentum (use the same parameter values as above) 3. Find the mean value and standard deviation ((Ar)? = (x?) - (x)?) for the particle coordinate 4. Find the mean value and standard deviation for the particle momentum 5. Calculate ArAp