
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/(4Å2)). 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. |