Physics 751 Homework # 11

Due Wednesday, December 3.

1. A spin-1/2 system is in the eigenstate of the operator with the largest possible eigenvalue. Find the probability that a measurement of S_z gives .

2. A spin-1/2 object is in an eigenstate of S_x with eigenvalue at time t = 0, the moment when a magnetic field B = B k is turned on (k being the unit vector in the z-direction, as usual). At time T the field is suddenly switched to B = B j. Another time interval T passes, and S_x is measured. With what probability will the value be found?

3. Find the matrix representation of the operators J_z, J_x, and J_y in the basis for angular momentum 3/2.

4. An angular momentum system j = 1 is in the state

.

What is the probability that a measurement of J_x of this system will yield zero?

Shankar: 14.4.6, 15.1.2, 15.2.5.