2.3 One-dimensional free rotator ca. 35/100 The Hamiltonian H (l , (p) = 12/21 describes a free rotator in one dimension, with angle (,0, angular momentum l, and moment of inertia I. a Solve its equations of motion, i.e., nd the nal conditions 1" = 103\"), go\" = 90(15\") for undetermined initial conditions l(t') = 1", 99(9) = 90". b In a real experimental setup, the initial conditions are never known to innite accuracy. If angle and angular momentum can only be determined up to tolerances (I), 0 /2 g (p' g /2, L/2 g l' g L/2, what is the corresponding normalized initial probability density distribution p(l", 99", t")? c With the help of the results of part a, calculate the time-evolved phase-space probability distribution p(l\