By evaluating the ``volume'' of the relevant region of its phase space, show that the number of microstates available to a rigid rotator with angular momentum ≤M is (M/ℏ)2. Hence determine the number of microstates that may be associated with the quantized angular momentum Mj={j(j+1)}ℏ, where j=0,1,2,… or 21,23,25,…. Interpret the result physically.
[Hint: It simplifies to consider motion in the variables θ and φ, with M2=pθ2+(pϕ/sinθ)2.]