Do 3 of the 4 problems.

• Problem 1:

  Two neutrons are confined two a cubical box whose sides are 1Å in length.  The particles interact strongly, whenever the distance between them is less than 10^-15m.  Approximate the interaction potential by V(r₁-r₂)=-(4pR³V₀/3)d(r₁-r₂), with R=10^-15m, and use perturbation theory to calculate the ground state energy and wave function.

• Problem 2:

  For the Nitrogen atom find the three terms in the LS coupling scheme which lie lowest in energy.

• Problem 3:

  In one dimension, the potential energy of an electron as a function of x is given by

  U(x)=-30eVexp(-x²/(4Ų)).

  Use the variational method to find the energy of the ground state in units of eV.

• Problem 4:

  Determine the differential scattering cross section s(q) in units of cm²/sr for a particle of mass m=9.1´10^-31kg incident on a spherically symmetric potential

  V(r)=0, 0<r<a, V(r)=V₀, a<r<b, V(r)=0, r>b,

  with a=0.05nm and b=0.1nm.  Let E=1eV and V₀=0.8eV.