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 Demonstrate that the operators defined in Equations (427)(429) are Hermitian, and
satisfy
the commutation relations (417).
 Prove the BakerHausdorff lemma, (447).
 Find the Pauli representations of the normalized eigenstates of
and
for
a spin
particle.
 Suppose that a spin
particle
has a spin vector that 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 spinstate
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 spinup state with respect to the
axis, determine the spinor
that 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 Angular Momentum
Previous: Spin Greater Than OneHalf
Richard Fitzpatrick
20130408