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

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

- Find the Pauli representations of the normalized eigenstates of and for
a spin- particle.
- 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
.

- 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 .

- 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 ?

- An electron is at rest in an oscillating magnetic field

where and are real positive constants.
- Find the Hamiltonian of the system.
- 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.
- Find the probability that a measurement of yields
the result as a function of time.
- 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