Do 3 of the 4 problems.
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.
For the Nitrogen atom find the three terms in the LS coupling scheme which lie lowest in energy.
In one dimension, the potential energy of an electron as a function of x is given by
U(x)=-30eVexp(-x2/(4Å2)).
Use the variational method to find the energy of the ground state in units of eV.
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.