   Next: Addition of Angular Momentum Up: Spin Precession Previous: Spin Precession

### Exercises

1. Find the Pauli representations of , , and for a spin-1 particle.

2. Find the Pauli representations of the normalized eigenstates of and for a spin- particle.
3. Suppose that a spin- particle has a spin vector which lies in the - plane, making an angle with the -axis. Demonstrate that a measurement of yields with probability , and with probability .

4. An electron is in the spin-state in the Pauli representation. Determine the constant by normalizing . If a measurement of is made, what values will be obtained, and with what probabilities? What is the expectation value of ? Repeat the above calculations for and .

5. Consider a spin- system represented by the normalized spinor in the Pauli representation, where and are real. What is the probability that a measurement of yields ?

6. An electron is at rest in an oscillating magnetic field where and are real positive constants.
1. Find the Hamiltonian of the system.
2. If the electron starts in the spin-up state with respect to the -axis, determine the spinor which represents the state of the system in the Pauli representation at all subsequent times.
3. Find the probability that a measurement of yields the result as a function of time.
4. What is the minimum value of required to force a complete flip in ?   Next: Addition of Angular Momentum Up: Spin Precession Previous: Spin Precession
Richard Fitzpatrick 2010-07-20