Angular momentum
1. Commutation relations involving angular momentum: Evaluate or establish the following commu-
tation relations involving angular momentum:
Note: ijk ljk = 2δil.
2. Rotation matrix for j = 1: Consider a system with j = 1.
.
3. (a) Energy of a spin- particle: A spin- particle is described by the Hamiltonian
,
(b) Particle in a central potential: A particle in a spherically symmetric potential is known to
be in the eigenstate |l,m of the operators Lˆ2 and Lˆz with eigenvalues l(l + 1)2 and m, respectively.
4. Expectation value in the singlet state: Suppose two spin- particles are known to be in the singlet
5. Addition of spin angular momentum: Consider a system composed of two particles, one with spin-
and another with spin-1.
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