1. The primary change in poing from translatioe ta rotation is forand in going from lanear moemenfum to asgular momentum. This change is signaficand as seen in the form of the momenhm operakors Fy=izMy=ih(xyyx) a. Civen the equation M=fj Obeain expressions for Ma,Ay and Mx in Cartesian coendinates. (M7 ks given above) b. In class we indicated Mx=i(xyyx)=iha and from a simple rotational diagram in the xy-plane we showed cos=rxx=rcossin=ryy=rsinr=(x2+y2)23 Wse this information asd the chain rale to show At=ihadA starting with the Cartesiae varsion of M2 gives abore. c. While it is obwious p^r,py=0 since x and y are independent variables, the same a not true for [Mx,My]. Show [Mx,My]=ihRx 4. Rationalive the values of [Ry,N7] and [M2,M7] withou doing the detals. e. Show that Mx,My, and Mx comaute with M2, whert M2=Mr2+My2+Mx2. Hint yoe cely have to do it fer any one of the three and use reasonits similar so part di. in where a =x0yo or z. f. Lsing the above revolts, what can we say abenat the possibelity of sinnaltancees cigenfunctions for M3+My,P3, and M27Can any of the pairs have simultanceses eigenfunctions