2. The angular momentum operator of a single particle (measured in units of h) is given by the expression 1 = - i[r x V]. (1) (a) Write down its components /; (i=x,yz) in rectangular coordinates. For the rest of this problem you will be guided through a calculation of the operators I; i = x, y, z, in spherical coordinates defined in a standard fashion: x = r sin 0 coso, y = r sin 0 sin p. z = r cose. (2) (b) Take an arbitrary function I and compute the partial derivatives d'/30 and d'P/dip expressing final results in terms of rectangular coordinates, partial derivatives d'l'/dx, d'/dy, d'W/dz and p = r sin0 = (3) introduced for convenience; it will not be present in final answers. Comparing the expression for d'P/dd with you result in part (a) determine Iz (c) Multiply your results in part (b) for d'l'/30 by x/p and for d'P/dd by -yz/p' and add the two resulting equation. Now you should be able to extract an expression for I,. What is it? (d) Using a suggestion in part (c) as a template of how to proceed, determine