29.16Sample Test Problems
- A hydrogen atom is in then= 5,^3 D 52 state. To which states is it allowed to decay via electric
dipole transitions? What will be the polarization for a photon emitted along thez-axis ifml
decreases by one unit in the decay?
- Derive the selection rules for radiative transitions between hydrogen atom states in the electric
dipole approximation. These are rules for the change inl,m, ands.
- State the selection rules for radiative transitions between hydrogen atom states in the electric
dipole approximation. These are rules for the allowed changes inl,m,s, and parity. They can
be easily derived from the matrix element given on the front of the test. Draw an energy level
diagram (up ton= 3) for hydrogen atoms in a weakBfield. Show the allowed E1 transitions
fromn= 3 ton= 1 on that diagram.
- Calculate the differential cross section,ddσΩ, for high energy scattering of particles of momentum
p, from a spherical shell delta function
V(r) =λ δ(r−r 0 )
Assume that the potential is weak so that perturbation theory can be used. Be sure to write
your answer in terms of the scattering angles.
- Assume that a heavy nucleus attractsK 0 mesons with a weak Yakawa potentialV(r) =Vr^0 e−αr.
Calculate the differential cross section,dσdΩ, for scattering high energyK 0 mesons (massmK)
from that nucleus. Give your answer in terms of the scattering angleθ.
