4. The commutation relations defining the angular momentum operators can be written as:[Lx, Ly] = ihLz;with similar equations for cyclic permutations of x, y, and z. Angular momentum raising and lowering operators can be defined as:(i) Show that[Ly, Lz] = ihLx;(ii) If ψ is an eigenfunction of Lz with eigenvalue mh, show that the state given by L ψ is also an eigenfunction of L, but with an eigenvalue of (m 1)h.(iii) In a Cartesian representation, the operator representing the z component of

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a) The fundamental commutation relations for orbital angular mo... | Filo