Write the Schrödinger equation for 3-dimensional rotations of a molecule (in spherical polar coordinates) in terms of the corresponding Hamiltonian operator and its eigenfunctions: (b) What are the eigenvalues of the energy corresponding to the Hamiltonian in part (a)? (c) Write the eigenvalue equation for the square of the total angular momentum (in spherical polar coordinates) in terms of the corresponding operator and its eigenfunctions: (d) Write the eigenvalue equation for the component of the angular momentum along a given (z) axis (in spherical polar coordinates) in terms of the corresponding operator and eigenfunctions: (e) Write the commutation relations that express the fact that only the magnitude of the angular momentum and one of its components (in rectangular Cartesian coordinates) can be simultaneously measured: (f) Write the commutation relations which indicate that the individual components of the angular momentum (in rectangular Cartesian coordinates) cannot be determined simultaneously: