• For the case of a small angle dø, write the matrices above with all matrix elements given as polynomials of do up to second order. In this limit, obtain the expression [R.(86), R,(8ø)] = R:(56²) – I. • Consider the quantum mechanical operators Dz(8ø) = I –J,86, and D.(8ø), Dy(Sø) similarly defined where Jr, Jy and J, are the components of the angular momentum vector J. Assuming that Dz(86), Dz(86) and Dy(86) have the same commutation relations as R(86), R,(86) and R:(86) above, obtain the commutation relations of Jr, Jy and J,. Namely: [Ji, J;] = iħeijk- From this, you will readily show that: [J?, JA] = 0 For i = x, y, z.

• For the case of a small angle dø, write the matrices above with all matrix elements given as polynomials of do up to second order. In this limit, obtain the expression [R.(86), R,(8ø)] = R:(56²) – I. • Consider the quantum mechanical operators Dz(8ø) = I –J,86, and D.(8ø), Dy(Sø) similarly defined where Jr, Jy and J, are the components of the angular momentum vector J. Assuming that Dz(86), Dz(86) and Dy(86) have the same commutation relations as R(86), R,(86) and R:(86) above, obtain the commutation relations of Jr, Jy and J,. Namely: [Ji, J;] = iħeijk- From this, you will readily show that: [J?, JA] = 0 For i = x, y, z.