A Guide to Physics Problems. Part 2. Thermodynamics, Statistical Physics, and Quantum Mechanics

b) From the definition of we deduce that

The matrix is the Hermitian conjugate of

c) Because and we can construct

d) To find the matrix we square each of the three

matrices and add them. Thisgives where is the 4 × 4 unit
matrix. This is what one expects, since the eigenvalue of is J(J + 1),
which is 15/4 whenJ = 3/2.

QUANTUM MECHANICS 273