Problem 1:

A one-dimensional periodic potential consists of a sequence of Dirac delta functions with a distance d between them.  (This is called the Dirac comb.)

.

Determine the energy eigenvalues of this potential.

Problem 2:

Consider a Fermi gas model of the nucleus consisting of independent proton and neutron Fermi gases.  Derive expressions for the Fermi energies of both the proton and the neutron gases consisting of N neutrons and Z protons respectively, where N+Z=A, the mass number of the nucleus.  If the radius of a nucleus is given by R=1.2A^1/3fm and m_p»m_n=1.6´10^-24g, calculate the numerical values of the Fermi energies for ¹⁹⁸Au.