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- Calculate the Clebsch-Gordon coefficients for adding spin one-half
to spin one.

- Calculate the Clebsch-Gordon coefficients for adding spin one
to spin one.

- An electron in a hydrogen atom occupies the combined spin
and position state whose wavefunction is

- What values would a measurement of
yield, and with
what probabilities?
- Same for
.
- Same for
.
- Same for
.
- Same for
.
- Same for
.
- What is the probability density for finding the electron at
,
,
?
- What is the probability density for finding the electron in the
spin up state (with respect to the
-axis) at radius
?

- In a low energy neutron-proton system (with zero orbital angular
momentum) the potential energy is given by

where
,
**
**
denotes the vector of the Pauli matrices of the neutron,
and
**
**
denotes the vector of the Pauli matrices of the proton. Calculate
the potential energy for the neutron-proton system:
- In the spin singlet (i.e., spin zero) state.
- In the spin triplet (i.e., spin one) state.

[Hint: Calculate the expectation value of
with respect to the overall spin state.]

- Consider two electrons in a spin singlet (i.e., spin zero) state.
- If a measurement of the spin of one of the electrons shows that it
is in the state with
, what is the probability that a
measurement of the
-component of the spin of the
other electron yields
?
- If a measurement of the spin of one of the electrons shows
that it is in the state with
, what is the probability that a
measurement of the
-component of the spin of the
other electron yields
?
- Finally, if electron 1 is in a spin state described by
, and
electron 2 is in a spin state described by
, what is
the probability that the two-electron spin state is a triplet (i.e., spin one) state?

** Next:** Time-Independent Perturbation Theory
** Up:** Addition of Angular Momentum
** Previous:** Analysis
Richard Fitzpatrick
2013-04-08