- A particle is in the state
.
Find the expected values of , , , and .
- A particle is in the state
.
If a measurement of the component of angular momentum is made, what are the possilbe outcomes
and what are the probabilities of each?
- Calculate the matrix elements
and
- The Hamiltonian for a rotor with axial symmetry is
where the are constant moments of inertia.
Determine and plot the eigenvalues of for dumbbell-like case that .
- Prove that
is only possible for .
- Write the spherical harmonics for in terms of the Cartesian coordinates , , and .
- A particle in a spherically symmetric potential has the wave-function
.
A measurement of is made.
What are the possible results and the probabilities of each?
If the measurement of yields , what are the possible measured values of
and what are the corresponding probabilities?
- The deuteron, a bound state of a proton and neutron with , has a binding energy of -2.18 MeV.
Assume that the potential is a spherical well with potential of for Fermis and zero potential outside.
Find the approximate value of using numerical techniques.

Jim Branson 2013-04-22